DILATION OF PROJECTIVE ISOMETRIC REPRESENTATION ASSOCIATED WITH UNITARY MULTIPLIER

Abstract

For a unital ∗-subalgebra of the space La(X) of all adjointable maps on a Hilbert B-module X with a C ∗-algebra B, we study unitary operator (in such algebra)-valued multiplier σ on a normal, generating subsemigroup S of a group G with its extension to G. A dilation of a projective isometric σ-representation of S is established as a projective unitary ρ-representation of G for a suitable unitary operator (in some algebra)-valued multiplier ρ associated with the multiplier σ which is explicitly constructed.

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