Hilbert Bimodules and Partial-Isometric Crossed Products by One Endomorphism

Hosseini, Abbas

doi:10.1080/1726037X.2012.10698609

Open Access Original Articles

Hilbert Bimodules and Partial-Isometric Crossed Products by One Endomorphism

Abbas Hosseiniahosseiniq@gmail.comDepartment of MathematicsIslamic Azad UniversityParand Branch, IranView full profile →

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pp. 71–90Vol. 10Issue 1May 2012DOI: 10.1080/1726037X.2012.10698609XML

Received:: 24 Feb 2011
Accepted:: 18 Jan 2012
Published Online:: 03 Jun 2013
Article type:: Original Articles
Language:: EN
Article no.:: 1726037X.2012.10698609
Pages:: 71–90

Abstract

Let α be an extendible endomorphism of a C* -algebra A, and let X be the Hilbert bimodule (1)A. We analyze the Toeplitz algebra of this Hilbert bimodule and we show that the partial-isometric crossed product A × ℕ is isomorphic to the Toeplitz algebra T. Then we have two crossed product exact sequences.

Keywords

Hilbert Bimodule extendible endomorphism partial isometry Toeplitz algebra

References

Adji, S.Oct 1996 . “ Invariant ideals of crossed products by semigroup of endomorphisms ” . In , Oct , 1 – 8 . Singapore: Springer-Verlag .
Adji, S., Laca, M., Nilsen, M. and Raeburn, I.1994 . Crossed products by semigruop of endomorphisms and the Toeplitz algebras of ordered gruoups . , 122 ( 4 ) : 1133 – 1141 .
S. Adji, PhD Thesis, Univ. of Newcastle, 1995.
Fowler, N. J. and Raeburn, I.1999 . The Toelitz algebras of a Hilbert bimodule . , 48 ( 1 ) : 155 – 181 .
Fowler, N. J., Muhly, P. and Raeburn, I.2003 . Representations of Cuntz-Pimsner Algebras . , 52 ( 3 ) : 569 – 605 .
Fowler, N. J.2002 . Discrete product systems of Hilbert bimodules . , 204 ( 2 ) : 335 – 375 .
Lindiarni, J. and Raeburn, I.2004 . Partial-isometric crossed products by semigroup of endomorphims . , 18 ( 1 ) : 61 – 87 .
Raeburn, I. and Williams, D. P.1998 . Morita equivalence and continuouos-trace *-algebras . , 60 Amer. Math. Soc., Providence
Murphy, Gerard J.1990 . , New York: Academic Press .
Wegge-Olsen, N. E.1993 . , Oxford: Oxford University Press .
Williams, Dana P.2007 . , Mathematical Surveys and Monographs Vol. 134 ,
Christopher Lance, E.1994 . , London Math. Soc. Lecture Note Series Vol. 210 , Cambridge: Cambridge Univ. Press .

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[1] Adji, S.Oct 1996 . “ Invariant ideals of crossed products by semigroup of endomorphisms ” . In , Oct , 1 – 8 . Singapore: Springer-Verlag .

[2] Adji, S., Laca, M., Nilsen, M. and Raeburn, I.1994 . Crossed products by semigruop of endomorphisms and the Toeplitz algebras of ordered gruoups . , 122 ( 4 ) : 1133 – 1141 .

[3] S. Adji, PhD Thesis, Univ. of Newcastle, 1995.

[4] Fowler, N. J. and Raeburn, I.1999 . The Toelitz algebras of a Hilbert bimodule . , 48 ( 1 ) : 155 – 181 .

[5] Fowler, N. J., Muhly, P. and Raeburn, I.2003 . Representations of Cuntz-Pimsner Algebras . , 52 ( 3 ) : 569 – 605 .

[6] Fowler, N. J.2002 . Discrete product systems of Hilbert bimodules . , 204 ( 2 ) : 335 – 375 .

[7] Lindiarni, J. and Raeburn, I.2004 . Partial-isometric crossed products by semigroup of endomorphims . , 18 ( 1 ) : 61 – 87 .

[8] Raeburn, I. and Williams, D. P.1998 . Morita equivalence and continuouos-trace *-algebras . , 60 Amer. Math. Soc., Providence

[9] Murphy, Gerard J.1990 . , New York: Academic Press .

[10] Wegge-Olsen, N. E.1993 . , Oxford: Oxford University Press .

[11] Williams, Dana P.2007 . , Mathematical Surveys and Monographs Vol. 134 ,

[12] Christopher Lance, E.1994 . , London Math. Soc. Lecture Note Series Vol. 210 , Cambridge: Cambridge Univ. Press .

Journal of Dynamical Systems and Geometric Theories

WoS JIF 2026 : 0.5 (Q3)

Hilbert Bimodules and Partial-Isometric Crossed Products by One Endomorphism

Abstract

Keywords

References