Central and Almost Constrained Subspaces of Banach Spaces

A New Class of Banach Sequence Spaces

On an atomic decomposition in Banach spaces

An atomic decomposition is considered in Banach space.  A method for constructing an atomic decomposition of Banach  space, starting with atomic decomposition of  subspaces  is presented. Some relations between them are established. The proposed method is used in the  study  of the  frame  properties of systems of eigenfunctions and associated functions of discontinuous differential operators.

On the Dimension of Almost Hilbertian Subspaces of Quotient Spaces

The question of the dimension of almost Hilbertian subspaces is resolved in [1] where it is shown that every Banach space E of dimension n possesses almost Hilbertian subspaces of dimension c(logn), where c is an absolute constant, and that this estimate is the best possible. When the net is spread wider to include quotient spaces and subspaces of quotient spaces we should expect to find instan...

Strictly Singular Uniform λ−Adjustment in Banach Spaces

Based on the recently introduced uniform λ−adjustment for closed subspaces of Banach spaces we extend the concept of the strictly singular and nitely strictly singular operators to the sequences of closed subspaces and operators in Banach spaces and prove theorems about lower semi Fredholm stability. We also state some new open questions related to strict singularity and the geometry of Banach ...

Maurey’s Factorization Theory for Operator Spaces

In Banach space theory probabilistic techniques play a central role. For example in the local theory of Banach spaces, geometric properties of finite dimensional subspaces are proved from probabilistic inequalities. The probabilistic approach not only enriched Banach space theory, but also introduced Banach space techniques in other areas such as probability or convex geometry. A famous instanc...