On the Extension of B. Sz.-Nagy's Dilation Theorem to Linear Pencils of Operators

Details On the Extension of B. Sz.-Nagy's Dilation Theorem to Linear Pencils of Operators On the Extension of B. Sz.-Nagy's Dilation Theorem to Linear Pencils of Operators

2000-02-28

arxiv.org/abs/math/0002234v1

Mathematics

Functional Analysis

LaTeX, 12 pages

Scientific paper

The explicit constructions of minimal isometric, and minimal unitary dilations of an arbitrary linear pencil of operators $T(\lambda)=T_0+\lambda T_1$ consisting of contractions on a separable Hilbert space for $|\lambda |=1$, which generalize the classical constructions (the case $T_1=0$), are presented. In contrast to the classical case these dilations are essentially non-unique.

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