Banach

banach@mathdept.okstate.edu

2549 discussions

Elton Lacey Funeral, Scholarship
by Dale Alspach 27 Jun '13

27 Jun '13

http://www.legacy.com/obituaries/theeagle/obituary.aspx?n=howard-lacey-elto… is a link to a newspaper obituary for Elton Lacey. It also gives details about the funeral. The family prefers donations to a scholarship fund rather than sending flowers. A link to a donation page is provided. Dale Alspach

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Dr. Howard Elton Lacey
by James Lacey 21 Jun '13

21 Jun '13

Just wanted to let the list know that my father Dr. Elton Lacey who was a Banach space researcher passed away today after a lengthy illness. Some of you may have known of him at the least. I have included a short summary of his life below. Thank you and best of luck to you all in your endeavors. Elton graduated from Leakey High School in 1955 and entered Texas A&M Univ. shortly thereafter. In the summer of 1957 he worked with the Corps of Engineers on the Mississippi river cutting transit lines for flood control projects. The first day there he went to the 4th St. Church of Christ and met his future wife Bonnie Brown and they were married August 1958 in Natchez, MS. That fall Elton continued his education at Abilene Christian Univ. where he received his B.A. in Mathematics in 1959 and his M.A. in Mathematics in 1960. Next Elton and Bonnie moved their family to Las Cruses, NM where Elton attended New Mexico State Univ. and earned his Ph.D. in Mathematics in 1963. In the summer of 1963 Elton worked at White Sands Missile Range in NM. That fall he returned to ACU as Assistant Professor. In the summer of 1964 he went to UT at Austin as an Asst. Professor. He was promoted to Assoc. Prof. in 1969 and full Prof. in 1974. He took leave from UT twice during his tenure. In the summer of 1966 and during the academic year of 1967-1968 Elton was at the Analysis Division of the Manned Space Craft Center. During the academic year of 1972-1973 Elton was at the Institute of Mathematics, Polish Academy of Science in Warsaw. While there Elton wrote letters home describing our experiences in Poland. His Aunt Cindy kept them and they were later typed up and turned into a family book. In 1974 he was promoted to Professor at UT Austin. When Dr. R. H. Bing returned to UT as Chairmen of Mathematics, Elton served as his Vice-Chairman. A number of his publications while at UT were with S. J. Bernau in Functional Analysis and Banach Spaces. He also published a book with Springer-Verlag, Berlin, NY in their prestigious Yellow Series, and another with UT Press and one with TAMU Press. In the summer of 1980 Elton taught math at the Free Univ. of Berlin, W. Germany. When he returned to Texas, he started as Prof. and Head of Mathematics, Texas A&M Univ., 1980-91. He served at Texas A&M Univ. from 1991-92 as Prof and Assoc. Dean. Later, he returned to his first love, teaching mathematics and retired in 2002. Upon retiring he was named a Prof. Emeritus of Mathematics. In the early 1990s Elton and Bonnie started working on family history. He was featured in the Dallas Morning News for using the internet for genealogy. Elton became an expert in Lacey family history and published several genealogy books including one on his maternal ancestors the Brices. He was a member of a number of heritage societies including the Sons of the American Revolution.

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Abstract of a paper by Miguel Martin
by alspach＠math.okstate.edu 07 Jun '13

07 Jun '13

This is an announcement for the paper "Norm-attaining compact operators" by Miguel Martin. Abstract: We show examples of compact linear operators between Banach spaces which cannot be approximated by norm attaining operators. This is the negative answer to an open question posed in the 1970's. Actually, any strictly convex Banach space failing the approximation property serves as the range space. On the other hand, there are examples in which the domain space has Schauder basis. It now makes sense to discuss sufficient conditions on the domain or the range space to ensure that every compact linear operator between them can be approximated by norm attaining operators. We get several basic results in this line and mention some open problems. Archive classification: math.FA Mathematics Subject Classification: Primary 46B20, Secondary 46B04, 46B45, 46B28, 47B07 Submitted from: mmartins(a)ugr.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1306.1155 or http://arXiv.org/abs/1306.1155

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Abstract of a paper by Denis Potapov and Fedor Sukochev
by alspach＠math.okstate.edu 07 Jun '13

07 Jun '13

This is an announcement for the paper "Frechet differentiability of Sp norms" by Denis Potapov and Fedor Sukochev. Abstract: One of the long standing questions in the theory of Schatten-von Neumann ideals of compact operators is whether their norms have the same differentiability properties as the norms of their commutative counterparts. We answer this question in the affirmative. A key technical observation underlying our proof is a discovery of connection between this question and recent affirmative resolution of L.S. Koplienko's conjecture concerning existence of higher order spectral shift functions. Archive classification: math.FA Submitted from: d.potapov(a)unsw.edu.au The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1306.0362 or http://arXiv.org/abs/1306.0362

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Abstract of a paper by Apostolos Giannopoulos, Pantelis Stavrakakis, Antonis Tsolomitis and Beatrice-Helen Vritsiou
by alspach＠math.okstate.edu 07 Jun '13

07 Jun '13

This is an announcement for the paper "Geometry of the $L_q$-centroid bodies of an isotropic log-concave measure" by Apostolos Giannopoulos, Pantelis Stavrakakis, Antonis Tsolomitis and Beatrice-Helen Vritsiou. Abstract: We study some geometric properties of the $L_q$-centroid bodies $Z_q(\mu )$ of an isotropic log-concave measure $\mu $ on ${\mathbb R}^n$. For any $2\ls q\ls\sqrt{n}$ and for $\varepsilon \in (\varepsilon_0(q,n),1)$ we determine the inradius of a random $(1-\varepsilon )n$-dimensional projection of $Z_q(\mu )$ up to a constant depending polynomially on $\varepsilon $. Using this fact we obtain estimates for the covering numbers $N(\sqrt{\smash[b]{q}}B_2^n,tZ_q(\mu ))$, $t\gr 1$, thus showing that $Z_q(\mu )$ is a $\beta $-regular convex body. As a consequence, we also get an upper bound for $M(Z_q(\mu ))$. Archive classification: math.FA math.MG Submitted from: apgiannop(a)math.uoa.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1306.0246 or http://arXiv.org/abs/1306.0246

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Abstract of a paper by Jamilson Ramos Campos
by alspach＠math.okstate.edu 07 Jun '13

07 Jun '13

This is an announcement for the paper "An abstract result on Cohen strongly summing operators" by Jamilson Ramos Campos. Abstract: We present an abstract result that characterizes the coincidence of certain classes of linear operators with the class of Cohen strongly summing linear operators. Our argument is extended to multilinear operators and, as a consequence, we establish a few alternative characterizations for the class of Cohen strongly summing multilinear operators. Archive classification: math.FA Remarks: 9 pages Submitted from: jamilson(a)dce.ufpb.br The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1305.7276 or http://arXiv.org/abs/1305.7276

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Abstract of a paper by D. Freeman, E. Odell, B. Sari, and Th. Schlumprecht
by alspach＠math.okstate.edu 07 Jun '13

07 Jun '13

This is an announcement for the paper "Equilateral sets in uniformly smooth Banach spaces" by D. Freeman, E. Odell, B. Sari, and Th. Schlumprecht. Abstract: Let $X$ be an infinite dimensional uniformly smooth Banach space. We prove that $X$ contains an infinite equilateral set. That is, there exists a constant $\lambda>0$ and an infinite sequence $(x_i)_{i=1}^\infty\subset X$ such that $\|x_i-x_j\|=\lambda$ for all $i\neq j$. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46B04 Remarks: 11 pages Submitted from: dfreema7(a)slu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1305.6750 or http://arXiv.org/abs/1305.6750

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Abstract of a paper by Richard Aron, Yun Sung Choi, Sun Kwang Kim, Han Ju Lee, and Miguel Martin
by alspach＠math.okstate.edu 07 Jun '13

07 Jun '13

This is an announcement for the paper "The Bishop-Phelps-Bollob\'as version of Lindenstrauss properties A" by Richard Aron, Yun Sung Choi, Sun Kwang Kim, Han Ju Lee, and Miguel Martin. Abstract: We study a Bishop-Phelps-Bollob\'as version of Lindenstrauss properties A and B. For domain spaces, we study Banach spaces $X$ such that $(X,Y)$ has the Bishop-Phelps-Bollob\'as property (BPBp) for every Banach space $Y$. We show that in this case, there exists a universal function $\eta_X(\eps)$ such that for every $Y$, the pair $(X,Y)$ has the BPBp with this function. This allows us to prove some necessary isometric conditions for $X$ to have the property. We also prove that if $X$ has this property in every equivalent norm, then $X$ is one-dimensional. For range spaces, we study Banach spaces $Y$ such that $(X,Y)$ has the Bishop-Phelps-Bollob\'as property for every Banach space $X$. In this case, we show that there is a universal function $\eta_Y(\eps)$ such that for every $X$, the pair $(X,Y)$ has the BPBp with this function. This implies that this property of $Y$ is strictly stronger than Lindenstrauss property B. The main tool to get these results is the study of the Bishop-Phelps-Bollob\'as property for $c_0$-, $\ell_1$- and $\ell_\infty$-sums of Banach spaces. Archive classification: math.FA Mathematics Subject Classification: Primary 46B20, Secondary 46B04, 46B22 Submitted from: mmartins(a)ugr.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1305.6420 or http://arXiv.org/abs/1305.6420

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Abstract of a paper by Tomasz Kobos
by alspach＠math.okstate.edu 07 Jun '13

07 Jun '13

This is an announcement for the paper "Equilateral dimension of some classes of normed spaces" by Tomasz Kobos. Abstract: An equilateral dimension of a normed space is a maximal number of pairwise equidistant points of this space. The aim of this paper is to study the equilateral dimension of certain classes of finite dimensional normed spaces. The well-known conjecture states that the equilateral dimension of any $n$-dimensional normed space is not less than $n+1$. By using an elementary continuity argument, we establish it in the following classes of spaces: permutation-invariant spaces, Orlicz-Musielak spaces and in one codimensional subspaces of $\ell^n_{\infty}$. For smooth and symmetric spaces, Orlicz-Musielak spaces satisfying an additional condition and every $(n-1)$-dimensional subspace of $\ell^{n}_{\infty}$ we also provide some weaker bounds on the equilateral dimension for every space which is sufficiently close to one of these. This generalizes the result of Swanepoel and Villa concerning the $\ell_p^n$ spaces. Archive classification: math.MG math.FA Mathematics Subject Classification: 46B85, 46B20, 52C17, 52A15, 52A20 Remarks: 12 pages Submitted from: tkobos(a)wp.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1305.6288 or http://arXiv.org/abs/1305.6288

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Abstract of a paper by Jameson Cahill, Peter G. Casazza, Jesse Peterson and Lindsey
by alspach＠math.okstate.edu 07 Jun '13

07 Jun '13

This is an announcement for the paper "Real phase retrieval by projections" by Jameson Cahill, Peter G. Casazza, Jesse Peterson and Lindsey. Abstract: The problem of recovering a vector from the absolute values of its inner products against a family of measurement vectors has been well studied in mathematics and engineering. A generalization of this phase retrieval problem also exists in engineering: recovering a vector from measurements consisting of norms of its orthogonal projections onto a family of subspaces. There exist semidefinite programming algorithms to solve this problem, but much remains unknown for this more general case. Can families of subspaces for which such measurements are injective be completely classified? What is the minimal number of subspaces required to have injectivity? How closely does this problem compare to the usual phase retrieval problem with families of measurement vectors? In this paper, we answer or make incremental steps toward these questions. We provide several characterizations of subspaces which yield injective measurements, and through a concrete construction, we prove the surprising result that phase retrieval can be achieved with $2M-1$ projections of arbitrary rank in $\HH_M$. Finally we present several open problems as we discuss issues unique to the phase retrieval problem with subspaces. Archive classification: math.FA Submitted from: lmwvh4(a)mail.missouri.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1305.6226 or http://arXiv.org/abs/1305.6226

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