Journal article
Numerical ranges of products and tensor products
Tôhoku mathematical journal, Vol.30(2), pp.257-262
01/01/1978
DOI: 10.2748/tmj/1178230029
Abstract
In this paper we study the relationship between the numerical ranges of Hubert space operators and those of their products and tensor products. Let &{3lf) denote the set of bounded linear operators on a complex Hubert space Sίf. For T e ^ ( ^ ) , W(T) denotes its numerical range, W(T) = {(Tx,x):\\x\\ = l}. For Γ, e ^ C ^ ) , 3 = 1, 2, it is clear that W(T, (x) T2) contains the set WTO WTO = {zfr: z, e W(T5\ j = 1, 2}; by the convexity of the numerical range, WiT^ ® T2) also contains its convex hull, co (WiT^-WiT,)) [11, Lemma 6.2]. We are interested in the conditions that guarantee WIT, (g) T2) = co (WiTJ W(T2)). We shall show that if either 2\ or T2 is normal, then g) T2) = cδ( WTO W(T2)) , where the bars denote the closure of the sets. This result follows from: Let A,Be^?(βέ?) be two commuting operators; if A or B is normal, then W(AB)^Έδ(W(A) W(B)).
Details
- Title: Subtitle
- Numerical ranges of products and tensor products
- Creators
- Elias S. W. Shiu - University of Manitoba
- Resource Type
- Journal article
- Publication Details
- Tôhoku mathematical journal, Vol.30(2), pp.257-262
- DOI
- 10.2748/tmj/1178230029
- ISSN
- 0040-8735
- eISSN
- 1881-2015
- Language
- English
- Date published
- 01/01/1978
- Academic Unit
- Statistics and Actuarial Science
- Record Identifier
- 9984257618102771
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