Strictly singular non-compact operators on a class of HI spaces

We present a method for constructing bounded strictly singular non-compact operators on mixed Tsirelson spaces defined either by the families (A_n) or (S_n) of a certain class, as well as on spaces built on them, including hereditarily indecomposable spaces.Comment: 19 page

Operators in tight by support Banach spaces

We answer the question of W.T. Gowers, giving an example of a bounded operator on a subspace of Gowers unconditional space which is not a strictly singular perturbation of a restriction of a diagonal operator. We make some observations on operators in arbitrary tight by support Banach space, showing in particular that in such space no two isomorphic infinitely dimensional subspaces form a direct sum.Comment: 17 pages. Revised version - added Remark 1.2, Theorem 2.10 and corresponding changes in the pape

Isomorphisms and strictly singular operators in mixed Tsirelson spaces

We study the family of isomorphisms and strictly singular operators in mixed Tsirelson spaces and their modified versions setting. We show sequential minimality of modified mixed Tsirelson spaces T_M[(\mc{S}_n,\theta_n)] satisfying some regularity conditions and present results on existence of strictly singular non-compact operators on subspaces of mixed Tsirelson spaces defined by the families (\mc{A}_n)_n and (\mc{S}_n)_n.Comment: 29 pages, no figure

Unconditionally saturated Banach space with the scalar-plus-compact property

We construct a Bourgain-Delbaen $\mathscr{L}_\infty$-space $\mathfrak{X}_{Kus}$ with strongly heterogenous structure: any bounded operator on $\mathfrak{X}_{Kus}$ is a compact perturbation of a multiple of the identity, whereas the space $\mathfrak{X}_{Kus}$ is saturated with unconditional basic sequences.Comment: The result about tightness removed,notation clarified and corrected, clarifying comments added, Journal of Functional Analysis, 201

A Banach space with an infinite dimensional reflexive quotient algebra L(X)/SS(X)

We construct a Banach space X of Gowers-Maurey type such that the algebra of bounded operators L(X) is a direct sum of an infinite dimensional reflexive Banach space and the operator ideal of strictly singular operators SS(X).Comment: 23 pages, minor corrections and simplifications with one essential simplification - replacing the auxiliary space Z with ell_

The Emotional Effect of Same Sex Grouping

The research question addressed in this project was, how do gender roles affect the achievement of school-aged children? It documents one teachers research in her fifth grade classroom by creating a curriculum related challenge that students worked on in mixed gender groups and same gender groups. The author documents the details of the research literature review in order to analyze and validate the study. The action research portion included surveys that students responded to, asking them to reflect over their experience. In conclusion, the author describes both successes and struggles of working with mixed and same gender groups and concludes that: males and females rated their experience significantly higher when working with their same gender peers