1,292 research outputs found
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
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 -space
with strongly heterogenous structure: any bounded operator
on is a compact perturbation of a multiple of the
identity, whereas the space 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 study of closed-circuit educational television at Hagerstown, Maryland
Thesis (Ed.M.)--Boston Universit
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