Fock Space Techniques in Tensor Algebras of Directed Graphs

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Fock Space Techniques in Tensor Algebras of Directed Graphs

Alvaro Arias

Source: Rocky Mountain J. Math. Volume 39, Number 4 (2009), 1089-1143.

First Page: Show

Primary Subjects: 46H25

Secondary Subjects: 47A20, 47D25, 47A57, 46M20

Keywords: Fock spaces; $C*$-correspondences; directed graphs

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.rmjm/1248269774
Digital Object Identifier: doi:10.1216/RMJ-2009-39-4-1089
Zentralblatt MATH identifier: 05587672
Mathematical Reviews number (MathSciNet): MR2524706

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References

A. Arias, Projective modules in Fock spaces, J. Operator Theory 52 (2004), 139-172.

Mathematical Reviews (MathSciNet): MR2091465

Zentralblatt MATH: 1078.46035

A. Arias and G. Popescu, Noncommutative interpolation and Poisson transforms, Israel J. Math. 115 (2000), 205-234.

Mathematical Reviews (MathSciNet): MR1749679

Zentralblatt MATH: 0967.47045

Digital Object Identifier: doi:10.1007/BF02810587

A. Arias and G. Popescu, Noncommutative interpolation and Poisson transforms II, Houston J. Math. 25 (1999), 79-98.

Mathematical Reviews (MathSciNet): MR1675377

Zentralblatt MATH: 0967.47046

W. Arveson, Subalgebras of $C^\ast $% -algebras III, Multivariable operator theory, Acta Math. 181 (1998), 159-228.

Mathematical Reviews (MathSciNet): MR1668582

Zentralblatt MATH: 0952.46035

Digital Object Identifier: doi:10.1007/BF02392585

D. Blecher, P. Muhly and V. Paulsen, Categories of operator modules (Morita equivalence and projective modules), Memoirs American Math. Soc. 143, 2000%), viii+94 pp.

Mathematical Reviews (MathSciNet): MR1645699

Zentralblatt MATH: 0966.46033

K. Davidson and D. Pitts, The algebraic structure of non-commutative analytic Toeplitz algebras, Math. Ann. 311 (1998), 275-303.

Mathematical Reviews (MathSciNet): MR1625750

Zentralblatt MATH: 0939.47060

Digital Object Identifier: doi:10.1007/s002080050188

R. Douglas and V. Paulsen, Hilbert modules over function algebras, %Pitman Research Notes in Mathematics Series, 217.% Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1989. %vi+130 pp.

Mathematical Reviews (MathSciNet): MR1028546

N. Fowler and I. Raeburn, The Toeplitz algebra of a Hilbert bimodule, Indiana Univ. Math. J. 48 (1999), 155-181.

Mathematical Reviews (MathSciNet): MR1722197

Zentralblatt MATH: 0938.47052

Digital Object Identifier: doi:10.1512/iumj.1999.48.1639

M. Jury and D. Kribs, Ideal structure in free semigroupoid algebras from directed graphs, J. Operator Theory 53 (2005), 273-302.

Mathematical Reviews (MathSciNet): MR2153149

Zentralblatt MATH: 1119.47312

--------, Partially isometric dilations of noncommuting $N$-tuples of operators, Proc. Amer. Math. Soc. 133 (2005), 213-222.

Mathematical Reviews (MathSciNet): MR2085172

Zentralblatt MATH: 1068.47013

Digital Object Identifier: doi:10.1090/S0002-9939-04-07547-1

E. Katsoulis and D. Kribs, Applications of the Wold decomposition to the study of row contractions associated with directed graphs, Trans. Amer. Math. Soc. 357 (2005), 3739-3755.

Mathematical Reviews (MathSciNet): MR2146647

Zentralblatt MATH: 1081.47019

Digital Object Identifier: doi:10.1090/S0002-9947-05-03692-5

--------, Isomorphisms of algebras associated with directed graphs, Math. Ann. 330 (2004), 709-728.

Mathematical Reviews (MathSciNet): MR2102309

Zentralblatt MATH: 1069.47072

Digital Object Identifier: doi:10.1007/s00208-004-0566-6

D. Kribs and S. Power, Free semigroupoid algebras, J. Ramanujan Math. Soc. 19 (2004), 117-159.

Mathematical Reviews (MathSciNet): MR2076898

Zentralblatt MATH: 1090.47060

E.C. Lance, Hilbert $C^\ast $-modules. A toolkit for operator algebraists, %London Mathematical Society Lecture Note Series, 210. Cambridge University Press, Cambridge, 1995. %x+130 pp.

Mathematical Reviews (MathSciNet): MR1325694

M. Michael, A class of $C^\ast$-algebras generalizing both Cuntz-Krieger algebras and crossed products by $\bf Z$, Free probability theory, %(Waterloo, ON, 1995), 189--212, Fields Institute Communications 12, Amer. Math. Soc., Providence, RI, 1997.

Mathematical Reviews (MathSciNet): MR1426840

Zentralblatt MATH: 0871.46028

P. Muhly and B. Solel, Tensor algebras over $% C^\ast $-correspondences: Representations, dilations, and $% C^\ast $-envelopes, J. Functional Anal. 158 (1998), 389-457.

Mathematical Reviews (MathSciNet): MR1648483

Zentralblatt MATH: 0912.46070

Digital Object Identifier: doi:10.1006/jfan.1998.3294

--------, Tensor algebras, induced representations, and the Wold decomposition, Canad. J. Math. 51 (1999), 850-880.

Mathematical Reviews (MathSciNet): MR1701345

--------, Hardy algebras $W^\ast $% -correspondences and interpolation theory, Math. Ann. 330 % (2004), 353-415.

Mathematical Reviews (MathSciNet): MR2089431

Zentralblatt MATH: 1066.46049

Digital Object Identifier: doi:10.1007/s00208-004-0554-x

--------, Duality of $W^\ast $% -correspondences and applications. Quantum probability and infinite dimensional analysis, QP-PQ: Quantum Probab. White Noise Anal. 18, World Science Publ., Hackensack, NJ, 2005, 399-414.

Mathematical Reviews (MathSciNet): MR2212463

W.L. Paschke, Inner product modules over $B^\ast$-algebras, Trans. Amer. Math. Soc. 182 (1973), 443-468.

Mathematical Reviews (MathSciNet): MR355613

Zentralblatt MATH: 0239.46062

Digital Object Identifier: doi:10.2307/1996542

JSTOR: links.jstor.org

G. Popescu, von Neumann inequality for $(B(\cal H)^n)_1$, Math. Scand. 68 (1991), 292-304.

Mathematical Reviews (MathSciNet): MR1129595

Zentralblatt MATH: 0774.46033

--------, On intertwining dilations for sequences of noncommuting operators, J. Math. Anal. Appl. 167 (1992), 382-402.

Mathematical Reviews (MathSciNet): MR1168596

Zentralblatt MATH: 0783.47006

Digital Object Identifier: doi:10.1016/0022-247X(92)90214-X

G. Popescu, Multi-analytic operators on Fock spaces, Math. Ann. 303 (1995), 31-46.

Mathematical Reviews (MathSciNet): MR1348353

Zentralblatt MATH: 0835.47015

Digital Object Identifier: doi:10.1007/BF01460977

--------, Poisson transforms on some $C^\ast $-algebras generated by isometries, J. Functional Anal. 161 (1999), 27-61.

Mathematical Reviews (MathSciNet): MR1670202

Zentralblatt MATH: 0933.46070

Digital Object Identifier: doi:10.1006/jfan.1998.3346

P. Quiggin, For which reproducing kernel Hilbert spaces is Pick's theorem true?, Integral Equations Operator Theory 16 (1993), 244-266.

Mathematical Reviews (MathSciNet): MR1205001

Zentralblatt MATH: 0779.30026

Digital Object Identifier: doi:10.1007/BF01358955

D. Sarason, Generalized interpolation in $H^\infty $, Trans. Amer. Math. Soc. 127 (1967), 179-203.

Mathematical Reviews (MathSciNet): MR208383

Zentralblatt MATH: 0145.39303

Digital Object Identifier: doi:10.2307/1994641

JSTOR: links.jstor.org

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