On a tensor product of weakly compact mappings
On a theorem of Gelfand and its local generalizations
In 1941, I. Gelfand proved that if a is a doubly power-bounded element of a Banach algebra A such that Sp(a) = 1, then a = 1. In [4], this result has been extended locally to a larger class of operators. In this note, we first give some quantitative local extensions of Gelfand-Hille’s results. Secondly, using the Bernstein inequality for multivariable functions, we give short and elementary proofs of two extensions of Gelfand’s theorem for m commuting bounded operators, , on a Banach space X.
On a theorem of H. P. Lotz on quasi-compactness of Markov operators
On a theorem of Jörgens and Chernoff concerning essential self-adjointness of Dirac operators.
On a theorem of Ky Fan
On a Theorem of Ky-Fan Type
On a theorem of L. Schwartz and its applications to absolutely summing operators
On a theorem of Lebow
On a theorem of Lebow and Mlak for several commuting operators
On a theorem of Rolewicz for semigroups of operators in locally convex spaces
On a theorem of Stinespring concerning integral operators of trace class.
On a theorem of Vesentini
Let 𝒜 be a Banach algebra over ℂ with unit 1 and 𝑓: ℂ → ℂ an entire function. Let 𝐟: 𝒜 → 𝒜 be defined by 𝐟(a) = 𝑓(a) (a ∈ 𝒜), where 𝑓(a) is given by the usual analytic calculus. The connections between the periods of 𝑓 and the periods of 𝐟 are settled by a theorem of E. Vesentini. We give a new proof of this theorem and investigate further properties of periods of 𝐟, for example in C*-algebras.
On a theorem of Zabczyk for semigroups of operators in locally convex spaces.
On a time-dependent subdifferential evolution inclusion with a nonconvex upper-semicontinuous perturbation.
On a time-dependent subdifferential evolution inclusion with Carathéodory perturbation
On an infinite-dimensional Hilbert space, we establish the existence of solutions for some evolution problems associated with time-dependent subdifferential operators whose perturbations are Carathéodory single-valued maps.
On a trace inequality for one-sided potentials and applications to the solvability of nonlinear integral equations.
On a two-step algorithm for hierarchical fixed point problems and variational inequalities.
On a type of matrix semigroup.
On a universality property of some abelian Polish groups
We show that every abelian Polish group is the topological factor group of a closed subgroup of the full unitary group of a separable Hilbert space with the strong operator topology. It follows that all orbit equivalence relations induced by abelian Polish group actions are Borel reducible to some orbit equivalence relations induced by actions of the unitary group.
On a variational property of integral functionals and related conjectures
The aim of this paper is to give the proofs of those results that in [4] were only announced, and, at the same time, to propose some possible developments, indicating some of the most significant open problems.