This is an announcement for the paper "On the ``Multiple of the Inclusion Plus Compact'' problem" by George Androulakis and Frank Sanacory. Abstract: The ``multiple of the inclusion plus compact problem'' which was posed by T.W.~Gowers in 1996 and Th.~Schlumprecht in 2003, asks whether for every infinite dimensional Banach space $X$ there exists a closed subspace $Y$ of $X$ and a bounded linear operator from $Y$ to $X$ which is not a compact perturbation of a multiple of the inclusion map from $Y$ to $X$. We give sufficient conditions on the spreading models of seminormalized basic sequences of a Banach space $X$ which guarantee that the ``multiple of the inclusion plus compact'' problem has an affirmative answer for $X$. Our results strengthen a previous result of the first named author, E.~Odell, Th.~Schlumprecht and N.~Tomczak-Jaegermann as well as a result of Th.~Schlumprecht. We give an example of a Hereditarily Indecomposable Banach space where our results apply. For the proof of our main result we use an extension of E.~Odell's Schreier unconditionality result for arrays. Archive classification: Functional Analysis Mathematics Subject Classification: 46A32, 47B07 The source file(s), lambdaipluscpt.tex: 114786 bytes, is(are) stored in gzipped form as 0701354.gz with size 28kb. The corresponding postcript file has gzipped size 203kb. Submitted from: giorgis@math.sc.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0701354 or http://arXiv.org/abs/math.FA/0701354 or by email in unzipped form by transmitting an empty message with subject line uget 0701354 or in gzipped form by using subject line get 0701354 to: math@arXiv.org.