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Fully representable and *-semisimple topological partial *-algebras

J.-P. Antoine, G. Bellomonte, C. Trapani (2012)

Studia Mathematica

We continue our study of topological partial *-algebras, focusing our attention on *-semisimple partial *-algebras, that is, those that possess a multiplication core and sufficiently many *-representations. We discuss the respective roles of invariant positive sesquilinear (ips) forms and representable continuous linear functionals, and focus on the case where the two notions are completely interchangeable (fully representable partial *-algebras) with the aim of characterizing a *-semisimple partial...

Fully summing mappings between Banach spaces

Mário C. Matos, Daniel M. Pellegrino (2007)

Studia Mathematica

We introduce and investigate the non-n-linear concept of fully summing mappings; if n = 1 this concept coincides with the notion of nonlinear absolutely summing mappings and in this sense this article unifies these two theories. We also introduce a non-n-linear definition of Hilbert-Schmidt mappings and sketch connections between this concept and fully summing mappings.

Function theory in sectors

Brian Jefferies (2004)

Studia Mathematica

It is shown that there is a one-to-one correspondence between uniformly bounded holomorphic functions of n complex variables in sectors of ℂⁿ, and uniformly bounded functions of n+1 real variables in sectors of ℝ n + 1 that are monogenic functions in the sense of Clifford analysis. The result is applied to the construction of functional calculi for n commuting operators, including the example of differentiation operators on a Lipschitz surface in ℝ n + 1 .

Functional calculi, regularized semigroups and integrated semigroups

Ralph deLaubenfels, Mustapha Jazar (1999)

Studia Mathematica

We characterize closed linear operators A, on a Banach space, for which the corresponding abstract Cauchy problem has a unique polynomially bounded solution for all initial data in the domain of A n , for some nonnegative integer n, in terms of functional calculi, regularized semigroups, integrated semigroups and the growth of the resolvent in the right half-plane. We construct a semigroup analogue of a spectral distribution for such operators, and an extended functional calculus: When the abstract...

Functional calculus for a class of unbounded linear operators on some non-archimedean Banach spaces

Dodzi Attimu, Toka Diagana (2009)

Commentationes Mathematicae Universitatis Carolinae

This paper is mainly concerned with extensions of the so-called Vishik functional calculus for analytic bounded linear operators to a class of unbounded linear operators on c 0 . For that, our first task consists of introducing a new class of linear operators denoted W ( c 0 ( J , ω , 𝕂 ) ) and next we make extensive use of such a new class along with the concept of convergence in the sense of resolvents to construct a functional calculus for a large class of unbounded linear operators.

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