Tensor Algebras, Induced Representations, and the Wold Decomposition

Canadian Journal of Mathematics - Tập 51 Số 4 - Trang 850-880 - 1999
Paul S. Muhly1, Baruch Solel2
1Department of Mathematics, University of Iowa, Iowa City, Iowa 52242, U.S.A.
2Department of Mathematics, Technion, 32000 Haifa, Israel

Tóm tắt

AbstractOur objective in this sequel to [18] is to develop extensions, to representations of tensor algebras overC*-correspondences, of two fundamental facts about isometries on Hilbert space: The Wold decomposition theorem and Beurling’s theorem, and to apply these to the analysis of the invariant subspace structure of certain subalgebras of Cuntz-Krieger algebras.

Từ khóa


Tài liệu tham khảo

10.1016/0022-247X(68)90122-4

Popescu, 1989, Characteristic functions for infinite sequences of noncommuting operators, J. Operator Theory, 22, 51

Lax, 1961, Translation invariant subspaces

Dixmier, 1977, C*-Algebras

10.1007/s002080050188

Popescu G. , A generalization of Beurling's theorem to a class of reflexive algebras. J. Operator Theory, to appear.

Doplicher, 1998, The C*-algebra of a Hilbert bimodule, Boll. Un.Mat. Ital. B (8), 1, 263

Fowler N. and Raeburn I. , The Toeplitz algebra of a Hilbert bimodule. Preprint.

10.1090/S0002-9904-1967-11845-7

Muhly, 1998, An algebraic characterization of boundary representations, 104

10.1016/0001-8708(74)90068-1

Popescu, 1998, NoncommutativeWold decompositions for semigroups of isometries, IndianaUniv.Math. J., 47, 277

10.1007/BF01460977

Davidson K. and Pitts D. , Invariant subspaces and hyper-reflexivity for free semigroup algebras, Proc. London Math. Soc., to appear.

Pimsner, 1997, Free Probability Theory, 12, 189

10.1016/0022-1236(90)90010-I

Beurling, 1949, On two problems concerning linear transformations in Hilbert space, ActaMath., 81, 239

10.1006/jfan.1998.3294

10.1512/iumj.1997.46.1182

10.1007/BF01388849

1969, Subalgebras of C*-algebras, ActaMath., 123, 141

Douglas, 1989, Research Notes in Math., 217

Halmos, 1961, Shifts on Hilbert spaces, J. Reine Angew.Math., 208, 102, 10.1515/crll.1961.208.102

10.1007/978-1-4612-0449-7

Muhly, 1995, Hilbert modules over operator algebras, Mem. Amer.Math. Soc., 117

10.1090/S0002-9947-1989-0972704-3