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Four characterizations of scalar-type operators with spectrum in a half-line

Peter Vieten (1997)

Studia Mathematica

C 0 -scalar-type spectrality criterions for operators A whose resolvent set contains the negative reals are provided. The criterions are given in terms of growth conditions on the resolvent of A and the semigroup generated by A. These criterions characterize scalar-type operators on the Banach space X if and only if X has no subspace isomorphic to the space of complex null-sequences.

Fourier analysis of a space of Hilbert-Shmidt operators. New Ha-plitz type operators.

Jaak Peetre (1990)

Publicacions Matemàtiques

If a group acts via unitary operators on a Hilbert space of functions then this group action extends in an obvious way to the space of Hilbert-Schmidt operators over the given Hilbert space. Even if the action on functions is irreducible, the action on H.-S. operators need not be irreducible. It is often of considerable interest to find out what the irreducible constituents are. Such an attitude has recently been advocated in the theory of "Ha-pliz" (Hankel + Toeplitz) operators. In this paper we...

Fourier analysis, Schur multipliers on S p and non-commutative Λ(p)-sets

Asma Harcharras (1999)

Studia Mathematica

This work deals with various questions concerning Fourier multipliers on L p , Schur multipliers on the Schatten class S p as well as their completely bounded versions when L p and S p are viewed as operator spaces. For this purpose we use subsets of ℤ enjoying the non-commutative Λ(p)-property which is a new analytic property much stronger than the classical Λ(p)-property. We start by studying the notion of non-commutative Λ(p)-sets in the general case of an arbitrary discrete group before turning to the...

Fractional iteration in the disk algebra: prime ends and composition operators.

Manuel D. Contreras, Santiago Díaz-Madrigal (2005)

Revista Matemática Iberoamericana

In this paper we characterize the semigroups of analytic functions in the unit disk which lead to semigroups of operators in the disk algebra. These characterizations involve analytic as well as geometric aspects of the iterates and they are strongly related to the classical theorem of Carathéodory about local connection and boundary behaviour of univalent functions.

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