Perfectness of Conelike *-Semigroups in ℚk

Nishio, Katsuyoshi; Sakakibara, Nobuhisa

doi:10.1002/1522-2616(200008)216:1<155::aid-mana155>3.0.co;2-x

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Unitary Dilation Of Several Contractions1

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2011

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Cited by 3 publications

(2 citation statements)

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“…Fortunately, there is a variety of * -semigroups which are semiperfect or operator semiperfect, and for which we can find convenient description of their dual * -semigroups and Laplace transforms (see e.g. [6,13,40,51,8,9,41,24,57]).…”

Section: Unitary Dilation Of Several Contractionsmentioning

confidence: 99%

Extending positive definiteness

Cichoń

Stochel

Szafraniec

2011

Trans. Amer. Math. Soc.

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Abstract. The main result of this paper gives criteria for extendibility of mappings defined on symmetric subsets of * -semigroups to positive definite ones. By specifying the mappings in question we obtain new solutions of relevant issues in harmonic analysis concerning truncations of some important multivariate moment problems, like complex, two-sided complex and multidimensional trigonometric moment problems. In addition, unbounded subnormality and existence of unitary power dilation of several contractions is treated as an application of our general scheme.

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Section: Unitary Dilation Of Several Contractionsmentioning

confidence: 99%

Extending positive definiteness

Cichoń

Stochel

Szafraniec

2011

Trans. Amer. Math. Soc.

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show abstract

“…The perfectness of conelike * -subsemigroups of finite-dimensional rational vector spaces with arbitrary involution (containing the zero of the space) was shown by Nishio and the second-mentioned author [21]. Since every * -semigroup which is generated by the union of its perfect * -subsemigroups is perfect [15], the assumption on the dimension is superfluous.…”

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confidence: 99%