Subproduct systems.
Subsequences of frames
Every frame in Hilbert space contains a subsequence equivalent to an orthogonal basis. If a frame is n-dimensional then this subsequence has length (1 - ε)n. On the other hand, there is a frame which does not contain bases with brackets.
Subseries in Banach spaces
Subsets of nonempty joint spectrum in topological algebras
We give a necessary and a sufficient condition for a subset of a locally convex Waelbroeck algebra to have a non-void left joint spectrum In particular, for a Lie subalgebra we have if and only if generates in a proper left ideal. We also obtain a version of the spectral mapping formula for a modified left joint spectrum. Analogous theorems for the right joint spectrum and the Harte spectrum are also valid.
Subsets of the unit ball the are separated by more than one
Subspace in Hermitean Spaces of Countable Dimension. II.
Subspace mixing properties of operators in with applications to Gluskin spaces
Subspace Weyl-Heisenberg Frames.
Subspaces and m-Products of Nearly Exotic Spaces.
Subspaces of mixed-norm spaces of holomorphic functions
Subspaces in Hermitean Spaces of Countable Dimension.
Subspaces of for that are admissible as kernels.
Subspaces of , p > 2, determined by partitions and weights
Many of the known complemented subspaces of have realizations as sequence spaces. In this paper a systematic approach to defining these spaces which uses partitions and weights is introduced. This approach gives a unified description of many well known complemented subspaces of . It is proved that the class of spaces with such norms is stable under (p,2) sums. By introducing the notion of an envelope norm, we obtain a necessary condition for a Banach sequence space with norm given by partitions...
Subspaces of which do not contain -isomorphically
Subspaces of which embed into
Subspaces of ℓ₂(X) and Rad(X) without local unconditional structure
It is shown that if a Banach space X is not isomorphic to a Hilbert space then the spaces ℓ₂(X) and Rad(X) contain a subspace Z without local unconditional structure, and therefore without an unconditional basis. Moreover, if X is of cotype r < ∞, then a subspace Z of ℓ₂(X) can be constructed without local unconditional structure but with 2-dimensional unconditional decomposition, hence also with basis.
Subspaces of smooth sequence spaces
Subspaces of the Bourgain-Delbaen space
It is shown that every infinite-dimensional closed subspace of the Bourgain-Delbaen space has a subspace isomorphic to some .
Subspaces with a common complement in a Banach space
We study the problem of the existence of a common algebraic complement for a pair of closed subspaces of a Banach space. We prove the following two characterizations: (1) The pairs of subspaces of a Banach space with a common complement coincide with those pairs which are isomorphic to a pair of graphs of bounded linear operators between two other Banach spaces. (2) The pairs of subspaces of a Banach space X with a common complement coincide with those pairs for which there exists an involution...