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- W385065284 abstract "Which bounded linear operator on a complex separable Hilbert space can be dilated to a unilateral shift? This is the problem we are going to address here. Recall that an operator A on space H is said to dilate (resp. power dilate) to operator B on K if there is an isometry V from H to K such that A = V * BV (resp. A n =V * B n V for all n > 1) or, equivalently, if B is unitarily equivalent to a 2-by-2 operator matrix (left[ {begin{array}{*{20}{c}} A & * * & * end{array} } right]) with A in its upper left corner (resp.B n is unitarily equivalent to (left[ {begin{array}{*{20}{c}} {{{A}^{n}}} & * * & * end{array} } right]) under the same unitary operator for all n>1). Theunilateral shift S k of multiplicity (k (1 leqslant k leqslant infty ) ) is the operator ({S_k}(x0,x1,x2,...) = (0,{x_0}{x_1}, ldots )onsumnolimits_{n = 0}^infty { oplus H with dim H = k.} )" @default.
- W385065284 created "2016-06-24" @default.
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- W385065284 date "2000-01-01" @default.
- W385065284 modified "2023-09-24" @default.
- W385065284 title "Dilation to Unilateral Shifts" @default.
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- W385065284 doi "https://doi.org/10.1007/978-3-0348-8417-4_35" @default.
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