A criterion for subharmonicity of a function of the spectrum
A direct sum representation
A discontinuous function does not operate on the real part of a function algebra
A discrete integral representation for polynomials of fixed maximal degree and their universal Korovkin closure.
A domination theorem for function algebras
A function algebra without any point derivation
A General Approach to the Notion of Silov Boundary.
A generalization of Gelfand-Mazur theorem.
A generalization of the Maligranda--Orlicz Lemma.
A generalized Bishop-Gončar construction
A geometric condition equivalent to commutativity in Banach algebras
A hierarchy in the family of real surjective functions
This expository paper focuses on the study of extreme surjective functions in ℝℝ. We present several different types of extreme surjectivity by providing examples and crucial properties. These examples help us to establish a hierarchy within the different classes of surjectivity we deal with. The classes presented here are: everywhere surjective functions, strongly everywhere surjective functions, κ-everywhere surjective functions, perfectly everywhere surjective functions and Jones functions. The...
A Künneth formula in topological homology and its applications to the simplicial cohomology of
We establish a Künneth formula for some chain complexes in the categories of Fréchet and Banach spaces. We consider a complex of Banach spaces and continuous boundary maps dₙ with closed ranges and prove that Hⁿ(’) ≅ Hₙ()’, where Hₙ()’ is the dual space of the homology group of and Hⁿ(’) is the cohomology group of the dual complex ’. A Künneth formula for chain complexes of nuclear Fréchet spaces and continuous boundary maps with closed ranges is also obtained. This enables us to describe explicitly...
A local algebra structure for of the polydisc
A maximal Abelian subalgebra of the Calkin algebra with the extension property.
A Maximal Algebra.
A maximal subalgebra of R(X).
A measure induced metric topology for a Banach algebra
A microlocal F. and M. Riesz theorem with applications.
Consider, by way of example, the following F. and M. Riesz theorem for Rn: Let μ be a finite measure on Rn whose Fourier transform μ* is supported in a closed convex cone which is proper, that is, which contains no entire line. Then μ is absolutely continuous (cf. Stein and Weiss [SW]). Here, as in the sequel, absolutely continuous means with respect to Lebesque measure. In this theorem one can replace the condition on the support of μ* by a similar condition on the wave front set WF(μ) of μ, while...
A model for some analytic Toeplitz operators
We present a change of variable method and use it to prove the equivalence to bundle shifts for certain analytic Toeplitz operators on the Banach spaces . In Section 2 we see this approach applied in the analysis of essential spectra. Some partial results were obtained in [9] in the Hilbert space case.