Locally compact semi-algebras generated by a commuting operator family.
Lucid operators on Banach spaces
l(Φ,φ) operators and (Φ,φ)-spaces.
A new class of linear and bounded operators is introduced. This class is more general than the classes of operators from [4], [5] and [8]. Using this class lΦ,φ we also introduce a class of locally convex spaces which is more general than the classes of the nuclear spaces [2], [3] and φ-nuclear spaces [6]. For this class of operators similar properties are established to those of the well known classes lp, lφ, lΦ and also the stability of the tensor product is proved. The stability of the tensor...
Maximal left ideals of the Banach algebra of bounded operators on a Banach space
M-Ideals In Banach Spaces.
M-ideals of compact operators in classical Banach spaces.
(Non-)amenability of ℬ(E)
In 1972, the late B. E. Johnson introduced the notion of an amenable Banach algebra and asked whether the Banach algebra ℬ(E) of all bounded linear operators on a Banach space E could ever be amenable if dim E = ∞. Somewhat surprisingly, this question was answered positively only very recently as a by-product of the Argyros-Haydon result that solves the “scalar plus compact problem”: there is an infinite-dimensional Banach space E, the dual of which is ℓ¹, such that . Still, ℬ(ℓ²) is not amenable,...
Non-Leibniz algebras
On a class of linear operators.
On a symbol of operators generating finite-dimensional algebras
On algebraic generation of B(X) by two subalgebras with square zero
On Berberian's representation
On bounded time-dependent perturbations of operator cosine functions.
On Hilbert-Schmidt spaces
On ideals of operators and of locally convex spaces.
On inclusion relations between Lorentz sequence spaces and inequalities of Lewis type.
On isomorphisms between certain subalgebras of B(X)
On joint spectra of operators on a Banach space isomorphic to its square
On p-absolutely summing operators acting on Banach lattices