Stochel, J. Dilability of sesquilinear form-valued kernels. (English) Zbl 0655.47007 Ann. Pol. Math. 48, No. 1, 1-30 (1988). Following the classical work of Sz.-Nagy on the dilation theory of Hilbert space operator-valued functions on unital *-semigroups, the author studies the dilatability of sesquilinear form-valued kernels on noninvolutory and nonunital semigroups, that is, functions C:S\(\times S\to F(X)\), where S is a semigroup and F(X) is the space of all sesquilinear forms over the vector space X with values in the underlying field F (\({\mathbb{R}}\) or \({\mathbb{C}}).\) The main theorem of this paper gives a necessay and sufficient condition for positive-definite kernels to be dilatable; it is some kind of a boundedness condition involving a new kernel \(\tilde C\) from (S\(\times S)\times (S\times S)\) to F(X) associated with C. From this main theorem follow other *-dilatability results on *-semigrops. The paper concludes with an example of a kernel which has a dilation but not a minimal one. Reviewer: Wu Pei Yuan Cited in 1 Document MSC: 47A20 Dilations, extensions, compressions of linear operators 47B38 Linear operators on function spaces (general) Keywords:minimal dilation; minimal factorization; dilation theory of Hilbert space operator-valued functions on unital *-semigroups; dilatability of sesquilinear form-valued kernels on noninvolutory and nonunital semigroups; positive-definite kernels; boundedness condition; *- dilatability results on *-semigrops PDFBibTeX XMLCite \textit{J. Stochel}, Ann. Pol. Math. 48, No. 1, 1--30 (1988; Zbl 0655.47007) Full Text: DOI