اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدNorms of idempotent Schur multipliers
123
0
0.0
(
0
)
تأليف
Rupert H. Levene
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Let D be a masa in B(H) where H is a separable Hilbert space. We find real numbers eta_0 < eta_1 < eta_2 < ... < eta_6 so that for every bounded, normal D-bimodule map {Phi} on B(H) either ||Phi|| > eta_6, or ||Phi|| = eta_k for some k <= 6. When D is totally atomic, these maps are the idempotent Schur multipliers and we characterise those with norm eta_k for 0 <= k <= 6. We also show that the Schur idempotents which keep only the diagonal and superdiagonal of an n x n matrix, or of an n x (n+1) matrix, both have norm 2/(n+1) cot(pi/(n+1)), and we consider the average norm of a random idempotent Schur multiplier as a function of dimension. Many of our arguments are framed in the combinatorial language of bipartite graphs.
قيم البحث
اقرأ أيضاً
We introduce partially defined Schur multipliers and obtain necessary and sufficient conditions for the existence of extensions to fully defined positive Schur multipliers, in terms of operator systems canonically associated with their domains. We us
e these results to study the problem of extending a positive definite function defined on a symmetric subset of a locally compact group to a positive definite function defined on the whole group.
We define the Schur multipliers of a separable von Neumann algebra M with Cartan masa A, generalising the classical Schur multipliers of $B(ell^2)$. We characterise these as the normal A-bimodule maps on M. If M contains a direct summand isomorphic t
o the hyperfinite II_1 factor, then we show that the Schur multipliers arising from the extended Haagerup tensor product $A otimes_{eh} A$ are strictly contained in the algebra of all Schur multipliers.
We consider the tensor product of the completely depolarising channel on $dtimes d$ matrices with the map of Schur multiplication by a $k times k$ correlation matrix and characterise, via matrix theory methods, when such a map is a mixed (random) uni
tary channel. When $d=1$, this recovers a result of OMeara and Pereira, and for larger $d$ is equivalent to a result of Haagerup and Musat that was originally obtained via the theory of factorisation through von Neumann algebras. We obtain a bound on the distance between a given correlation matrix for which this tensor product is nearly mixed unitary and a correlation matrix for which such a map is exactly mixed unitary. This bound allows us to give an elementary proof of another result of Haagerup and Musat about the closure of such correlation matrices without appealing to the theory of von Neumann algebras.
Various norms can be defined on a Krein space by choosing different underlying fundamental decompositions. Some estimates of norms on Krein spaces are discussed and few results in Bognars paper are generalized.
In the present paper the unconditional convergence and the invertibility of multipliers is investigated. Multipliers are operators created by (frame-like) analysis, multiplication by a fixed symbol, and resynthesis. Sufficient and/or necessary condit
ions for unconditional convergence and invertibility are determined depending on the properties of the analysis and synthesis sequences, as well as the symbol. Examples which show that the given assertions cover different classes of multipliers are given. If a multiplier is invertible, a formula for the inverse operator is determined. The case when one of the sequences is a Riesz basis is completely characterized.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
