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Polar Decompositions of C 0(N) Contractions

Authors:	Pei Yuan Wu

Institution:	(1) Department of Applied Mathematics, National Chiao Tung University, Hsinchu, 300, Taiwan

Abstract:	Let A be a bounded linear operator on a complex separable Hilbert space H. We show that A is a C₀(N) contraction if and only if $A = u{\left( {I - {\sum {^{d}_{{j = 1}} r_{j} (x_{i} \otimes x_{j} )} }} \right)}$ , where U is a singular unitary operator with multiplicity $d \leq N,0 < r_1 , \ldots ,r_d \leq 1$ and x₁, . . . , x_d are orthonormal vectors satisfying $\bigvee \left\{ {U^k x_j :k \geq 0,1 \leq j \leq d} \right\} = H$ . For a C₀(N) contraction, this gives a complete characterization of its polar decompositions with unitary factors.

Keywords:	Primary 47A45 Secondary 47A20 15A23
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