Far East Journal of Mathematical Sciences (FJMS)

The Far East Journal of Mathematical Sciences (FJMS) publishes original research papers and survey articles in pure and applied mathematics, statistics, mathematical physics, and other related fields. It welcomes application-oriented work as well.

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TIPS ON BOUNDED DIFFERENTIAL OPERATOR CALCULUS FOR SOME C*-ALGEBRAS

Authors

  • Takahiro Sudo

Keywords:

derivation, inner derivation, matrix algebra, C*-algebra, unilateral shift, Toeplitz algebra

DOI:

https://doi.org/10.17654/0972087123002

Abstract

We study a general theory of bounded (or inner) derivations in C*-algebras from our point of view, as an account of some interest with some elementary elements. In particular, we obtain an index theory formula for the Toeplitz C*-algebra as in our sense.

Received: November 11, 2022
Accepted: December 13, 2022

References

Ola Bratteli and Derek W. Robinson, Operator Algebras ands Quantum Statistical Mechanics 1, TMP, Second ed., Springer, (1979, 1987).

B. E. Johnson and A. M. Sinclair, Continuity of derivations and a problem of Kaplansky, Amer. J. Math. 90 (1968), 1067-1073.

R. V. Kadison, Derivations on operator algebras, Ann. Math. 83 (1966), 280-293.

A. Kishimoto, Dissipations and derivations, Commun. Math. Phys. 47 (1976), 25-32.

Gerard J. Murphy, C*-algebras and Operator Theory, Academic Press, 1990.

S. Sakai, On a conjecture of Kaplansky, Tohoku Math. J. 12 (1960), 31-33.

S. Sakai, Derivations of W*-algebra, Ann. Math. 83 (1966), 273-278.

Shoichiro Sakai, Operator Algebras in Dynamical Systems, Encyclopedia of Math. and its Appl. 41, Cambridge, 1991.

Published

2022-12-30

Issue

Section

Articles

How to Cite

TIPS ON BOUNDED DIFFERENTIAL OPERATOR CALCULUS FOR SOME C*-ALGEBRAS. (2022). Far East Journal of Mathematical Sciences (FJMS), 140(1), 27-46. https://doi.org/10.17654/0972087123002

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