Atlas: Wedge Operators Between Locally Convex Spaces by Miguel Friz

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Functional Analysis Valencia 2000
July 3-7, 2000
Technical University of Valencia (UPV) and University of Valencia (UV)
Valencia, Spain

Organizers
R.M. Aron (Kent State U., USA), K.D. Bierstedt (U. Paderborn, Germany), J. Bonet (UPV), J. Cerdà (U. Barcelona, Spain), H. Jarchow (U. Zürich, Switzerland), M. Maestre (UV), J. Schmets (U. Liège, Belgium)

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Wedge Operators Between Locally Convex Spaces
by
Miguel Friz
Universidad Politécnica de Valencia

Let E₁, E₂, E₃ and E₄ be quasicomplete, barrelled locally convex spaces. Let L: E₃ --> E₄ and R: E₁ --> E₂ be continuous linear operators. The wedge operator R /\ L : L_b(E₂, E₃) --> L_b(E₁, E₄) is the continuous linear operator defined by

(R /\ L)(T) : = L T R, T in L(E₂, E₃)

.

In case the spaces E_i, i=1, ..., 4, are Banach spaces, the wedge operator has been studied by Vala [2] and Saksman, Tylli [1]. We analyze when the operator R /\ L is bounded, compact, weakly compact, and maps bounded sets into precompact or weakly compact sets. Applications to spaces of vector-valued sequences, and to composition operators on spaces of vector-valued holomorphic functions will be mentioned.

References.

[1] E. Saksman , H. Tylli Weak essential spectra of multiplication operators on spaces of bounded linear operators, Math. Ann. 299 (1994) p. 299-309.

[2] K. Vala On compact sets of compact operators, Ann. Acd. Sci. Fenn. Ser. A I. Math 351 (1964).

We report on research done under the advice of J. Bonet.

(P)

Date received: April 12, 2000