Open AccessALGEBRAIC EQUIVALENCE OF QUASINORMAL OPERATORS
Author(s) -
Kung-Yeu Chen
Publication year - 1994
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.25.1994.4429
Subject(s) - mathematics , sigma , equivalence (formal languages) , algebraic number , combinatorics , operator (biology) , pure mathematics , mathematical analysis , physics , biochemistry , chemistry , repressor , quantum mechanics , transcription factor , gene
Let $T_j =N_j\oplus( S\otimes A_j)$ be quasinormal, where $N_j$ is normal and $A_j$ is a positive definite operator, $j = 1, 2$. We show that $T_1$ is algebraically equivalent to $T_2$ if and only if $\sigma(A_1) =\sigma(A_2)$ and $\sigma(N_1)\backslash\sigma_{ap}(S\otimes A_1) =\sigma(N_2)\backslash\sigma_{ap}(S\otimes A_2)$. This generalizes the corresponding result for normal and isometric operators.