Vol. 65, No. 2, 1976

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The centraliser of E λF

Anthony William Wickstead

Vol. 65 (1976), No. 2, 563–571

If E is a real Banach space then (E) is the space of all bounded linear operators on E, and 𝒵(E) the subspace of M-bounded operators, i.e. the centraliser of E. Two Banach spaces E and F are considered as well as the tensor product E λF. There is a natural mapping of the algebraic tensor product 𝒵(E) ⊙𝒵(F) into 𝒵(E λF). It is shown that 𝒵(E λF) is precisely the strong operator closure, in (E λF), of its image.

Mathematical Subject Classification 2000
Primary: 46M05
Secondary: 46L20
Received: 18 November 1974
Revised: 17 March 1976
Published: 1 August 1976
Anthony William Wickstead