Approximation of some unbounded quasirepresentations of amenable groups several open problems
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As is well known, every bounded quasirepresentation of an amenable group in a dual Banach space admits an approximation by an ordinary representation, and the quality of this approximation depends on the defect of the quasirepresentation and on the bound for the norms of the quasirepresentation operators. We discuss a special case in which an unbounded quasirepresentation certainly admits an approximation by an ordinary representation such that the quality of the approximation depends on the defect of the quasirepresentation only and illustrate the result by an application to two-sided sequences of bounded Banach space operators satisfying some inequalities.
Abstract
As is well known, every bounded quasirepresentation of an amenable group in a dual Banach space admits an approximation by an ordinary representation, and the quality of this approximation depends on the defect of the quasirepresentation and on the bound for the norms of the quasirepresentation operators. We discuss a special case in which an unbounded quasirepresentation certainly admits an approximation by an ordinary representation such that the quality of the approximation depends on the defect of the quasirepresentation only and illustrate the result by an application to two-sided sequences of bounded Banach space operators satisfying some inequalities.
참고문헌 (6)
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