Tomasz Kania

Uniqueness of the maximal ideal of the Banach algebra of bounded operators on C([0,ω1])

Let ω1 be the smallest uncountable ordinal. By a result of Rudin, bounded operators on the Banach space C([0,ω1) have a natural representation as [0,ω1]×[0,ω1]-matrices. Loy and Willis observed that the set of operators whose final column is continuous when viewed as a scalar-valued function on [0,ω1] defines a maximal ideal of codimension one in the Banach algebra B(C([0,ω1])) of bounded operators on C([0,ω1]). We give a coordinate-free characterization of this ideal and deduce from it that B(C([0,ω1])) contains no other maximal ideals. We then obtain a list of equivalent conditions describing the strictly smaller ideal of operators with separable range, and finally we investigate the structure of the lattice of all closed ideals of B(C([0,ω1])).

Uncountable sets of unit vectors that are separated by more than 1

Let

A weak*-topological dichotomy with applications in operator theory

X

Finite generation in C*-algebras and Hilbert C*-modules

be a Banach space. We study the circumstances under which there exists an uncountable set

THE IDEAL OF WEAKLY COMPACTLY GENERATED OPERATORS ACTING ON A BANACH SPACE

\mathcal A\subset X

Maximal left ideals of the Banach algebra of bounded operators on a Banach space

of unit vectors such that

Steinhaus' lattice-point problem for Banach spaces

\|x-y\|>1

Uniqueness of the maximal ideal of operators on the ℓ p -sum of ℓ∞ n (n ∈ N ) for 1 < p< ∞

for distinct

Operators on two Banach spaces of continuous functions on locally compact spaces of ordinals

x,y\in \mathcal A

Symmetrically separated sequences in the unit sphere of a Banach space

. We prove that such a set exists if