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

A study of closed-circuit educational television at Hagerstown, Maryland

Thesis (Ed.M.)--Boston Universit

On a Question of Haskell P. Rosenthal Concerning a Characterization of c_0 and ℓ_p

The following property of a normalized basis in a Banach space is considered: any normalized block sequence of the basis has a subsequence equivalent to the basis. Under uniformity or other natural assumptions, a basis with this property is equivalent to the unit vector basis of c_0 or ℓ_p. An analogous problem concerning spreading models is also addressed

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