Multipliers of A ∗ -Algebras
Copyright policy )Multipliers of A ∗ -Algebras
Let A be an A*-algebra of the first kind with C*-algebra completion 9W. It is known that if A is dual then A2 is dense in A and the Banach algebras ML(A) and ML(%) of left multipliers of A and 9I are algebra isomorphic. In this note it is proved that ML(A) and ML(%) are topologically algebra isomorphic when A is an arbitrary A*-algebra of the first kind such that A2 is dense in A. As a consequence, it follows that every left multiplier of a replete Hilbert algebra A is automatically continuous.
General theory of \(C^*\)-algebras, Algebras of operators on Banach spaces and other topological linear spaces, Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX), A*-Algebra, Linear operators in \({}^*\)-algebras, C*-Algebra Completion, Hilbert Algebra, Left Multipliers, Topologically Algebra Isomorphic, Automatically Continuous, Hilbert algebras
General theory of \(C^*\)-algebras, Algebras of operators on Banach spaces and other topological linear spaces, Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX), A*-Algebra, Linear operators in \({}^*\)-algebras, C*-Algebra Completion, Hilbert Algebra, Left Multipliers, Topologically Algebra Isomorphic, Automatically Continuous, Hilbert algebras
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