Displaying similar documents to “Some remarks on the uniform approximation property in Banach spaces”

Ideals of finite rank operators, intersection properties of balls, and the approximation property

Åsvald Lima, Eve Oja (1999)

Studia Mathematica

Similarity:

We characterize the approximation property of Banach spaces and their dual spaces by the position of finite rank operators in the space of compact operators. In particular, we show that a Banach space E has the approximation property if and only if for all closed subspaces F of c 0 , the space ℱ(F,E) of finite rank operators from F to E has the n-intersection property in the corresponding space K(F,E) of compact operators for all n, or equivalently, ℱ(F,E) is an ideal in K(F,E). ...

Some more weak Hubert spaces

Alec Edgington (1991)

Studia Mathematica

Similarity:

We construct, by a variation of the method used to construct the Tsirelson spaces, a new family of weak Hilbert spaces which contain copies of l₂ inside every subspace.

Trace and determinant in Banach algebras

Bernard Aupetit, H. Mouton (1996)

Studia Mathematica

Similarity:

We show that the trace and the determinant on a semisimple Banach algebra can be defined in a purely spectral and analytic way and then we obtain many consequences from these new definitions.

Characterization of weak type by the entropy distribution of r-nuclear operators

Martin Defant, Marius Junge (1993)

Studia Mathematica

Similarity:

The dual of a Banach space X is of weak type p if and only if the entropy numbers of an r-nuclear operator with values in a Banach space of weak type q belong to the Lorentz sequence space ℓ s , r with 1/s + 1/p + 1/q = 1 + 1/r (0 < r < 1, 1 ≤ p, q ≤ 2). It is enough to test this for Y = X*. This extends results of Carl, König and Kühn.

The decomposability of operators relative to two subspaces

A. Katavolos, M. Lambrou, W. Longstaff (1993)

Studia Mathematica

Similarity:

Let M and N be nonzero subspaces of a Hilbert space H satisfying M ∩ N = {0} and M ∨ N = H and let T ∈ ℬ(H). Consider the question: If T leaves each of M and N invariant, respectively, intertwines M and N, does T decompose as a sum of two operators with the same property and each of which, in addition, annihilates one of the subspaces? If the angle between M and N is positive the answer is affirmative. If the angle is zero, the answer is still affirmative for finite rank operators but...