Spectral commutativity of multioperators

0376825 - MÚ 2013 RIV RS eng J - Článek v odborném periodiku
Cho, M. - Müller, Vladimír
Spectral commutativity of multioperators.
Functional Analysis, Approximation and Computation. Roč. 4, č. 1 (2012), s. 29-33. ISSN 1821-410X
Grant CEP: GA ČR(CZ) GA201/06/0128
Výzkumný záměr: CEZ:AV0Z10190503
Klíčová slova: criss-cross commuting * spectral commutativity
Kód oboru RIV: BA - Obecná matematika
http://operator.pmf.ni.ac.rs/www/pmf/publikacije/faac/2012/2012-4-1/faac-4-1-3.pdf

We give an example of commuting pairs A = (A1;A2), B = (B1; B2) of matrices such that AB := (A1B1;A2B2) and BA := (B1A1; B2A2) are commuting pairs but T(AB) , T(BA); moreover, T(AB) n f(z;w) : zw = 0g , T(BA) n f(z;w) : zw = 0g. Further, we show that T(AB) = T(BA) if A and B are criss-cross commuting n-tuples of operators and A is normal. This gives a positive answer to a problem studied in [2].
Trvalý link: http://hdl.handle.net/11104/0209133