In this paper, we give an extension of the orthogonality results to dominant operators and p-hyponormal or log-hyponormal operators, also we will generalize some commutativity results. AMS 2000 Mathematics Subject Classification. 47B47, 47A30, 47B20.

In this paper we develop a natural generalization of Schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. We prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. We prove that the operators of a dual ov-basis are continuous. We also dene the concepts of Bessel, Hilbert ov-basis and obta...

We investigate the relationship between complex symmetry of composition operators C ϕ f = ∘ induced on classical Hardy space H 2 ( D ) by an analytic self-map open unit disk and its Koenigs eigenfunction. A generalization orthogonality known as conjugate-orthogonality will play a key role in this work. show that if is Schröder map (fixes point ∈ with 0 < | ′ 1 σ eigenfunction, then symmetric on...