منابع مشابه
Complete Spectral Sets and Numerical Range
We define the complete numerical radius norm for homomorphisms from any operator algebra into B(H), and show that this norm can be computed explicitly in terms of the completely bounded norm. This is used to show that if K is a complete Cspectral set for an operator T , then it is a complete M -numerical radius set, where M = 12 (C + C −1). In particular, in view of Crouzeix’s theorem, there is...
متن کاملThe Spectral Scale and the Numerical Range
Suppose that c is an operator on a Hilbert Space H such that the von Neumann algebra N generated by c is finite. Let τ be a faithful normal tracial state on N and set b1 = (c+ c )/2 and b2 = (c− c)/2i. Also write B for the spectral scale of {b1, b2} relative to τ . In previous work by the present authors, some joint with Nik Weaver, B has been shown to contain considerable spectral information ...
متن کاملDecomposing numerical ranges along with spectral sets
This note is to indicate the new sphere of applicability of the method developed by Mlak as well as by the author. Restoring those ideas is summoned by current developments concerning K-spectral sets on numerical ranges. The decomposition of numerical ranges the title refers to is, see [13, p. 42], W(A⊕B) = conv(W(A) ∪ W(B)); (1) it can be proved for any two Hilbert space operators A and B. The...
متن کاملMinkowski product of convex sets and product numerical range
Let K1,K2 be two compact convex sets in C. Their Minkowski product is the set K1K2 = {ab : a ∈ K1, b ∈ K2}. We show that the set K1K2 is star-shaped if K1 is a line segment or a circular disk. Examples for K1 and K2 are given so that K1 and K2 are triangles (including interior) and K1K2 is not star-shaped. This gives a negative answer to a conjecture by Puchala et. al concerning the product num...
متن کاملThe Spectral Scale and the k–Numerical Range
Suppose that c is a linear operator acting on an n-dimensional complex Hilbert Space H, and let τ denote the normalized trace on B(H). Set b1 = (c + c )/2 and b2 = (c − c)/2i, and write B for the the spectral scale of {b1, b2} with respect to τ . We show that B contains full information about Wk(c), the k-numerical range of c for each k = 1, . . . , n. We then use our previous work on spectral ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2017
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/13801