caa a22 4500 467931917 CHVBK 20180406152946.0 cr unu---uuuuu 170328e20061201xx s 000 0 eng 10.1007/s00020-006-1438-0 doi (NATIONALLICENCE)springer-10.1007/s00020-006-1438-0 Wu Pei Department of Applied Mathematics, National Chiao Tung University, 300, Hsinchu, Taiwan aut Polar Decompositions of C 0( N ) Contractions [Elektronische Daten] [Pei Wu] 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, . . . , xd 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. Birkhäuser Verlag, Basel, 2006 C 0( N ) contraction nationallicence polar decomposition nationallicence singular unitary operator nationallicence compression of the shift nationallicence finite multiplicity nationallicence defect index nationallicence Integral Equations and Operator Theory Birkhäuser-Verlag; http://www.birkhauser.ch 56/4(2006-12-01), 559-569 0378-620X 56:4<559 2006 56 20 https://doi.org/10.1007/s00020-006-1438-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00020-006-1438-0 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Wu Pei Department of Applied Mathematics, National Chiao Tung University, 300, Hsinchu, Taiwan aut NATIONALLICENCE 773 0- Integral Equations and Operator Theory Birkhäuser-Verlag; http://www.birkhauser.ch 56/4(2006-12-01), 559-569 0378-620X 56:4<559 2006 56 20 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer