is generated in strong operator topology by two of its elements
Bade's theorem on the uniformly closed algebra generated by a Boolean algebra
Banach Algebra of Bounded Complex-Valued Functionals
In this article, we describe some basic properties of the Banach algebra which is constructed from all bounded complex-valued functionals.
Banach ideals of p-compact operators.
Banach-Lie algebras of compact operators
Beschränkte Operatoren: Bemerkungen zu einer Arbeit von P. Uss
Bilinear mappings and operator ideals
Boolean Algebras of Commuting Projections.
Boolean algebras of projections and ranges of spectral measures [Book]
Burnside's Theorem for the Fréchet Space .
Can ever be amenable?
It is known that is not amenable for p = 1,2,∞, but whether or not is amenable for p ∈ (1,∞) ∖ 2 is an open problem. We show that, if is amenable for p ∈ (1,∞), then so are and . Moreover, if is amenable so is for any index set and for any infinite-dimensional -space E; in particular, if is amenable for p ∈ (1,∞), then so is . We show that is not amenable for p = 1,∞, but also that our methods fail us if p ∈ (1,∞). Finally, for p ∈ (1,2) and a free ultrafilter over ℕ, we exhibit...
Closed ideals in the Banach algebra of operators on a Banach space
In general, little is known about the lattice of closed ideals in the Banach algebra ℬ(E) of all bounded, linear operators on a Banach space E. We list the (few) Banach spaces for which this lattice is completely understood, and we give a survey of partial results for a number of other Banach spaces. We then investigate the lattice of closed ideals in ℬ(F), where F is one of Figiel's reflexive Banach spaces not isomorphic to their Cartesian squares. Our main result is that this lattice is uncountable....
Compact non-nuclear operator problem
Compressible operators and the continuity of homomorphisms from algebras of operators
The notion of a compressible operator on a Banach space, E, derives from automatic continuity arguments. It is related to the notion of a cartesian Banach space. The compressible operators on E form an ideal in ℬ(E) and the automatic continuity proofs depend on showing that this ideal is large. In particular, it is shown that each weakly compact operator on the James' space, J, is compressible, whence it follows that all homomorphisms from ℬ(J) are continuous.
Connection between the algebra of kernels on the sphere and the Volterra algebra on the one-sheeted hyperboloid : holomorphic “perikernels”
Derivations into iterated duals of Banach algebras
We introduce two new notions of amenability for a Banach algebra A. The algebra A is n-weakly amenable (for n ∈ ℕ) if the first continuous cohomology group of A with coefficients in the n th dual space is zero; i.e., . Further, A is permanently weakly amenable if A is n-weakly amenable for each n ∈ ℕ. We begin by examining the relations between m-weak amenability and n-weak amenability for distinct m,n ∈ ℕ. We then examine when Banach algebras in various classes are n-weakly amenable; we study...
Dimensional gradations and cogradations of operator ideals. The weak distance between Banach-spaces
Distirbution of eigenvalues and nuclearity
Dual Banach algebras: representations and injectivity
We study representations of Banach algebras on reflexive Banach spaces. Algebras which admit such representations which are bounded below seem to be a good generalisation of Arens regular Banach algebras; this class includes dual Banach algebras as defined by Runde, but also all group algebras, and all discrete (weakly cancellative) semigroup algebras. Such algebras also behave in a similar way to C*- and W*-algebras; we show that interpolation space techniques can be used in place of GNS type arguments....
operators between normed spaces