Representations of semi direct products of groups
S. Sankaran (1970)
Compositio Mathematica
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S. Sankaran (1970)
Compositio Mathematica
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Detlev Poguntke (1993)
Studia Mathematica
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There is constructed a compactly generated, separable, locally compact group G and a continuous irreducible unitary representation π of G such that the image π(C*(G)) of the group C*-algebra contains the algebra of compact operators, while the image of the -group algebra does not containany nonzero compact operator. The group G is a semidirect product of a metabelian discrete group and a “generalized Heisenberg group”.
Ryszard Szwarc (1989)
Studia Mathematica
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F. GREENLEAF, M. MOSKOWITZ (1970/71)
Mathematische Annalen
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Wojciech Banaszczyk (1983)
Studia Mathematica
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Vlastimil Dlab (1960)
Czechoslovak Mathematical Journal
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Béla Nagy (2013)
Studia Mathematica
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Two characterizations of the reductivity of a cyclic normal operator in Hilbert space are proved: the equality of the sets of cyclic and *-cyclic vectors, and the equality L²(μ) = P²(μ) for every measure μ equivalent to the scalar-valued spectral measure of the operator. A cyclic subnormal operator is reductive if and only if the first condition is satisfied. Several consequences are also presented.
Froelich, John, Mathes, Ben (1995)
The New York Journal of Mathematics [electronic only]
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