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banach@mathdept.okstate.edu

June 2013

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Abstract of a paper by David Alonso-Gutierrez, Soeren Christensen, Markus Passenbrunner, and Joscha Prochno
by alspach＠math.okstate.edu 07 Jun '13

07 Jun '13

This is an announcement for the paper "On the Distribution of Random variables corresponding to norms" by David Alonso-Gutierrez, Soeren Christensen, Markus Passenbrunner, and Joscha Prochno. Abstract: Given a normalized Orlicz function $M$ we provide an easy formula for a distribution such that, if $X$ is a random variable distributed accordingly and $X_1,...,X_n$ are independent copies of $X$, then the expected value of the p-norm of the vector $(x_iX_i)_{i=1}^n$ is of the order $\| x \|_M$ (up to constants dependent on p only). In case $p=2$ we need the function $t\mapsto tM'(t) - M(t)$ to be $2$-concave and as an application immediately obtain an embedding of the corresponding Orlicz spaces into $L_1[0,1]$. We also provide a general result replacing the $\ell_p$-norm by an arbitrary $N$-norm. This complements some deep results obtained by Gordon, Litvak, Sch\"utt, and Werner. We also prove a result in the spirit of their work which is of a simpler form and easier to apply. All results are true in the more general setting of Musielak-Orlicz spaces. Archive classification: math.FA math.PR Mathematics Subject Classification: 46B09, 46B07, 46B45, 60B99 Submitted from: joscha.prochno(a)jku.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1305.1442 or http://arXiv.org/abs/1305.1442

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Abstract of a paper by Marek Cuth
by alspach＠math.okstate.edu 07 Jun '13

07 Jun '13

This is an announcement for the paper "Simultaneous projectional skeletons" by Marek Cuth. Abstract: We prove the existence of a simultaneous projectional skeleton for certain subspaces of $\mathcal{C}(K)$ spaces. This generalizes a result on simultaneous projectional resolutions of identity proved by M. Valdivia. We collect some consequences of this result. In particular we give a new characterization of Asplund spaces using the notion of projectional skeleton. Archive classification: math.FA Mathematics Subject Classification: 46B26, 54D30 Submitted from: cuthm5am(a)karlin.mff.cuni.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1305.1438 or http://arXiv.org/abs/1305.1438

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