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SECOND-ORDER NONCOMMUTATIVE DIFFERENTIAL AND LIPSCHITZ STRUCTURES DEFINED BY A CLOSED SYMMETRIC OPERATOR

Part of: Topological algebras, normed rings and algebras, Banach algebras Linear spaces and algebras of operators

Published online by Cambridge University Press:  25 November 2015

S. J. BHATT  and
MEETAL M. SHAH
S. J. BHATT*
Affiliation:
Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar, Gujarat 388120, India email [email protected]
MEETAL M. SHAH
Affiliation:
Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar, Gujarat 388120, India email [email protected]
*
✉[email protected]
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Abstract

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The Banach $^{\ast }$-operator algebras, exhibiting the second-order noncommutative differential structure and the noncommutative Lipschitz structure, that are determined by the unbounded derivation and induced by a closed symmetric operator in a Hilbert space, are explored.

Keywords

second-order noncommutative differential structuresymmetric operatornoncommutative Lipschitz structure

MSC classification

Primary: 47L40: Limit algebras, subalgebras of $C^*$-algebras
Secondary: 46H99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 100 , Issue 2 , April 2016 , pp. 145 - 162
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

References

Bhatt, S. J., ‘Stinespring representability and Kadison Schwarz inequality in non unital Banach ∗ -algebras and applications’, Proc. Math. Sci. Indian Acad. Sci. 108 (1998), 283–303.CrossRefGoogle Scholar
Bhatt, S. J., Inoue, A. and Ogi, H., ‘Differential structure in C ∗ -algebras’, J. Operator Theory 66(2) (2011), 301–334.Google Scholar
Bhatt, S. J., Karia, D. J. and Shah, M. M., ‘On a class of smooth Frechet sub algebras of C ∗ -algebras’, Proc. Math. Sci. Indian Acad. Sci. 123(3) (2013), 393–414.CrossRefGoogle Scholar
Blackadar, B. A. and Cuntz, J., ‘Differential Banach algebras norms and smooth sub algebras of C ∗ -algebras’, J. Operator Theory 26 (1991), 255–282.Google Scholar
Connes, A., Non Commutative Geometry (Academic Press, London and San Diego, 1994).Google Scholar
Kissin, E. and Shulman, V., ‘Differential properties of some dense subalgebras of C ∗ -algebras’, Proc. Edinb. Math. Soc. (2) 37(3) (1994), 399–422.CrossRefGoogle Scholar
Kissin, E. and Shulman, V., ‘Differential Banach ∗ -algebras of compact operators associated with symmetric operators’, J. Funct. Anal. 156 (1998), 1–29.Google Scholar
Kissin, E. and Shulman, V., ‘Dual spaces and isomorphisms of some differential Banach algebras of operators’, Pacific J. Math. 90 (1999), 329–359.Google Scholar
Kissin, E. and Shulman, V., ‘Differential Schatten ∗ -algebras, approximation properties and approximate identities’, J. Operator Theory 45 (2001), 303–334.Google Scholar
Rudin, W., Functional Analysis (McGraw-Hill Inc., New York, 1973).Google Scholar
Sakai, S., Operator Algebras in Dynamical Systems (Cambridge University Press, Cambridge–New York–Melbourne, 1991).Google Scholar
Weaver, N., ‘Lipschitz algebras and derivations of von Neumann algebras’, J. Funct. Anal. 139 (1996), 261–300.CrossRefGoogle Scholar
Weaver, N., ‘Lipschitz algebras and derivations II. Exterior differentiation’, J. Funct. Anal. 178 (2000), 64–112.Google Scholar