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Invariant subspaces on multiply connected domains.

Ali Abkar, Hakan Hedenmalm (1998)

Publicacions Matemàtiques

The lattice of invariant subspaces of several Banach spaces of analytic functions on the unit disk, for example the Bergman spaces and the Dirichlet spaces, have been studied recently. A natural question is to what extent these investigations carry over to analogously defined spaces on an annulus. We consider this question in the context of general Banach spaces of analytic functions on finitely connected domains Ω­. The main result reads as follows: Assume that B is a Banach space of analytic functions...

Invertibility in tensor products of Q-algebras

Seán Dineen, Pablo Sevilla-Peris (2002)

Studia Mathematica

We consider, using various tensor norms, the completed tensor product of two unital lmc algebras one of which is commutative. Our main result shows that when the tensor product of two Q-algebras is an lmc algebra, then it is a Q-algebra if and only if pointwise invertibility implies invertibility (as in the Gelfand theory). This is always the case for Fréchet algebras.

Invertibility preserving linear mappings into M₂(ℂ)

M. H. Shirdarreh Haghighi (2008)

Studia Mathematica

We study discontinuous invertibility preserving linear mappings from a Banach algebra into the algebra of n × n matrices and give an explicit representation of such a mapping when n = 2.

Isometries and automorphisms of the spaces of spinors.

F. J. Hervés, J. M. Isidro (1992)

Revista Matemática de la Universidad Complutense de Madrid

The relationships between the JB*-triple structure of a complex spin factor S and the structure of the Hilbert space H associated to S are discussed. Every surjective linear isometry L of S can be uniquely represented in the form L(x) = mu.U(x) for some conjugation commuting unitary operator U on H and some mu belonging to C, |mu|=1. Automorphisms of S are characterized as those linear maps (continuity not assumed) that preserve minimal tripotents in S and the orthogonality relations among them.

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