A Spectral Mapping Theorem for Holomorphic Functions.
Algebras of Toeplitz operators with oscillating symbols.
This paper is devoted to Banach algebras generated by Toeplitz operators with strongly oscillating symbols, that is, with symbols of the form b[eia(x)] where b belongs to some algebra of functions on the unit circle and a is a fixed orientation-preserving homeomorphism of the real line onto itself. We prove the existence of certain interesting homomorphisms and establish conditions for the normal solvability, Fredholmness, and invertibility of operators in these algebras.
Continuity of spectrum and spectral radius in algebras of operators
Derivations of quasi -algebras.
Double multipliers on topological algebras.
Fourier-like methods for equations with separable variables
It is well known that a power of a right invertible operator is again right invertible, as well as a polynomial in a right invertible operator under appropriate assumptions. However, a linear combination of right invertible operators (in particular, their sum and/or difference) in general is not right invertible. It will be shown how to solve equations with linear combinations of right invertible operators in commutative algebras using properties of logarithmic and antilogarithmic mappings. The...
Fredholm Theory Relative to a Banach Algebra Homomorphism.
Green's formula for right invertible operators
Hemi-Multiplicative Operators and Related Operators in Finite-Dimensional Algebras
J-subspace lattices and subspace M-bases
The class of J-lattices was defined in the second author’s thesis. A subspace lattice on a Banach space X which is also a J-lattice is called a J- subspace lattice, abbreviated JSL. Every atomic Boolean subspace lattice, abbreviated ABSL, is a JSL. Any commutative JSL on Hilbert space, as well as any JSL on finite-dimensional space, is an ABSL. For any JSL ℒ both LatAlg ℒ and (on reflexive space) are JSL’s. Those families of subspaces which arise as the set of atoms of some JSL on X are characterised...
Logarithmic and antilogarithmic mappings [Book]
Moyennes de fonctions et opérateurs multiplicativement liés
Multiplicity theory
Multipliers and local spectral theory
Non-Leibniz algebras
Numerical range preserving operators on a Banach algebra
On reflexive subobject lattices and reflexive endomorphism algebras
In this paper we study the reflexive subobject lattices and reflexive endomorphism algebras in a concrete category. For the category Set of sets and mappings, a complete characterization for both reflexive subobject lattices and reflexive endomorphism algebras is obtained. Some partial results are also proved for the category of abelian groups.
On the o-Spectrum of Order Bounded Operators.
On the structure of self adjoint algebra of finite strict multiplicity.
On the Translation Invariance of Wavelet Subspaces.