Bhatt, S. J. ; Fragoulopoulou, M. ; Inoue, A.
(2006)
*Existence of spectral well-behaved ^{*}-representations*
Journal of Mathematical Analysis and Applications, 317
(2).
pp. 475-495.
ISSN 0022-247X

Full text not available from this repository.

Official URL: http://www.sciencedirect.com/science/article/pii/S...

Related URL: http://dx.doi.org/10.1016/j.jmaa.2005.09.016

## Abstract

There are several cases, where an m^{*}-seminorm _{p} is defined
on a ^{*}-subalgebra of a given ^{*}-algebra A. This may lead to the
construction of an unbounded ^{*}-representation of A. Such
m^{*}-seminorms are called unbounded. Given an unbounded
m^{*}-seminorm_{p} of a ^{*}-algebra A, the concept of
a _{p}-spectral ^{*}-representation of A is introduced and studied in
connection to well-behaved ^{*}-representations. More precisely, the existence of (p-)
spectral well-behaved ^{*}-representations is investigated on
^{*}-algebras and locally convex ^{*}-algebras in terms of certain
properties of Ptak function, closely related to hermiticity and C^{*}-spectrality of the
^{*}-subalgebras on which this function is defined. Various examples in diverse classes of
locally convex algebras illuminate the elaborated results.

Item Type: | Article |
---|---|

Source: | Copyright of this article belongs to Elsevier Science. |

Keywords: | Spectral and p-spectral^{*}-representation; Well-behaved
^{*}-representation; Ptak Function; Hermitian Algebra |

ID Code: | 59696 |

Deposited On: | 07 Sep 2011 05:21 |

Last Modified: | 07 Sep 2011 05:21 |

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