research10.1016/0022-1236(86)90084-4

On operators preserving commutativity

Abstract

AbstractLet L(X) be the algebra of all bounded operators on a non-trivial complex Banach space X and F: L(X) → L(X) a bijective linear operator such that F and F−1 both send commuting pairs of operators into commuting pairs. Then, either F(A) = σUAU−1 + p(A) I, or F(A) = σUA′U−1 + p(A) I, where p is a linear functional on L(X), U is a bounded linear bijective operator between the appropriate two spaces, σ is a complex constant, and A′ is the adjoint of A. The form of an operator F for which F and F−1 both send projections of rank one into projections of rank one is also determined

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This paper was published in Elsevier - Publisher Connector .

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