排序方式: 共有17条查询结果,搜索用时 15 毫秒
1.
If a and b are trace-class operators, and if u is a partial isometry, then , where ∥⋅∥1 denotes the norm in the trace class. The present paper characterises the cases of equality in this Young inequality, and
the characterisation is examined in the context of both the operator and the Hilbert–Schmidt forms of Young's inequality.
Received: 20 December 2001 / Revised version: 11 July 2002 / Published online: 10 February 2003
Mathematics Subject Classification (2000): 47A63, 15A60 相似文献
2.
Douglas Farenick 《Journal of Pure and Applied Algebra》2008,212(10):2358-2367
The Witt Extension Theorem states that the unitary group of a finite-dimensional vector space V equipped with a nondegenerate hermitian form acts transitively on the pseudosphere induced by the form. We provide a new, constructive proof of this result for finite-dimensional vector spaces V over R, C, or H. This constructive proof is then used to prove a similar result for the unitary group of a finitely generated free right module over an abelian AW∗-algebra. The topology of these unitary groups is examined and as an application we determine the homotopy groups π1 and π2 of the induced real, complex, and quaternionic pseudospheres. 相似文献
3.
The C*-envelope of the 3-dimensional operator system generated by an irreducible periodic weighted unilateral shift operator is determined. 相似文献
4.
This paper characterises those hyponormal Toeplitz operators on the Hardy space of the unit circle among all Toeplitz operators that have polynomial symbols with circulant-type sets of coefficients.Supported in part by The Natural Sciences and Engineering Research Council of CanadaSupported in part by BSRI-96-1420 and KOSEF 94-0701-02-01-3 相似文献
5.
6.
D. R. Farenick 《Linear and Multilinear Algebra》1994,37(1):131-138
Those operators on Hilbert space that always have normal restrictions or compressions to subspaces of dimension 2 are described. The representation of the approximate point spectrum introduced by S. K. Berberian is shown to represent approximate restrictions in higher dimensions as well. 相似文献
7.
Douglas R. Farenick 《Proceedings of the American Mathematical Society》1996,124(11):3381-3390
Motivated by the classical results of G. Frobenius and O. Perron on the spectral theory of square matrices with nonnegative real entries, D. Evans and R. Høegh-Krohn have studied the spectra of positive linear maps on general (noncommutative) matrix algebras. The notion of irreducibility for positive maps is required for the Frobenius theory of positive maps. In the present article, irreducible positive linear maps on von Neumann algebras are explicitly constructed, and a criterion for the irreducibility of decomposable positive maps on full matrix algebras is given.
8.
Douglas R. Farenick Woo Young Lee 《Transactions of the American Mathematical Society》1996,348(10):4153-4174
This paper concerns algebraic and spectral properties of Toeplitz operators , on the Hardy space , under certain assumptions concerning the symbols . Among our algebraic results is a characterisation of normal Toeplitz opertors with polynomial symbols, and a characterisation of hyponormal Toeplitz operators with polynomial symbols of a prescribed form. The results on the spectrum are as follows. It is shown that by restricting the spectrum, a set-valued function, to the set of all Toeplitz operators, the spectrum is continuous at , for each quasicontinuous . Secondly, we examine under what conditions a classic theorem of H. Weyl, which has extensions to hyponormal and Toeplitz operators, holds for all analytic functions of a single Toeplitz operator with continuous symbol.
9.
Douglas Farenick 《Linear algebra and its applications》2011,435(4):769-1369
This paper is an exposition of W.B. Arveson’s complete invariant for the unitary similarity of complex, irreducible matrices. 相似文献
10.
Douglas R. Farenick Phillip B. Morenz 《Transactions of the American Mathematical Society》1997,349(5):1725-1748