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A weaker condition for normality

1994
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Glasgow Mathematical Journal
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Definitions. Throughout dK will denote a separable complex Hilbert space, and X will denote a complex Banach space. The set of bounded linear operators on X is denoted by B(X), and the set of all projections (that is, idempotent operators) on X by Proj(^f). Suppose that 9 is a Banach algebra of complex functions on some subset S c C , and that the functions e n (z) = z" lie in SF. Then by an 9 functional calculus we shall mean a Banach algebra homomorphism ip :&-+B (X) such that y>(e n ) = e n

doi:10.1017/s0017089500030792
fatcat:4ztwesdy4zd5vo3f7oli32x6fa