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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
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The C*-envelope of the 3-dimensional operator system generated by an irreducible periodic weighted unilateral shift operator is determined. 相似文献
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We define a discrete groupW(E) associated to a faithful normal conditional expectationE : M N forN M von Neuman algebras. This group shows the relation between the unitary groupU
N and the normalizerN
E ofE, which can be also considered as the isotropy of the action of the unitary groupU
M ofM onE. It is shown thatW(E) is finite if dimZ(N)< and bounded by the index in the factor case. Also sharp bounds of the order ofW(E) are founded.W(E) appears as the fibre of a covering space defined on the orbit ofE by the natural action of the unitary group ofM. W(E) is computed in some basic examples. 相似文献
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Martin Argerami Fernando Szechtman Ryan Tifenbach 《Linear and Multilinear Algebra》2007,55(6):515-520
The problem of whether Tate's trace is linear or not is reduced to a special case. 相似文献
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The problem of whether Tate's trace is linear or not is reduced to a special case. 相似文献
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We prove a contractive version of the Schur-Horn theorem for submajorization in II1 factors that complements some previous results on the Schur-Horn theorem within this context. We obtain a reformulation of a conjecture of Arveson and Kadison regarding a strong version of the Schur-Horn theorem in II1 factors in terms of submajorization and contractive orbits of positive operators. 相似文献
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