Decomposing numerical ranges along with spectral sets
نویسنده
چکیده
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 other decomposition is that of the spectrum of a function algebra related to a Hilbert space operator. These are the two leading topics of the current paper.
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