On Equivalences of Some Classes of Operators in Hilbert Space
Abstract
The study explores various classes of operators introduced by different researchers, including
n-normal, (n;m)-normal, k-quasi-(n;m)- normal, n-hyponormal, and (n;m)-hyponormal
operators. Notably, the class of (n;m)-hyponormal operators, defined by specifc inequalities,
is introduced, along with the concept of (n;m)-unitary quasiequivalence. The research
also introduces the novel concept of (n;m)-binormal operators, characterized by
specifc commutation conditions, and examines their properties, unitary equivalence, and
closure under summations. Additionally, the class of skew (n;m)-binormal operators are
introduced and investigated independently, highlighting their unique properties and unitary
equivalence. The study concludes with a summary, conclusions, and suggestions for
future research, providing a comprehensive overview of the diverse classes of operators
studied and their implications.
Publisher
University of Nairobi
Rights
Attribution-NonCommercial-NoDerivs 3.0 United StatesUsage Rights
http://creativecommons.org/licenses/by-nc-nd/3.0/us/Collections
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