Department of Mathematics, Islamic Azad University, Central Tehran Branch, PO. Code 13185-768, Tehran, Iran.
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 obtain some characterizations of them. We study orthonormal
and Riesz ov-bases for Hilbert spaces. Finally we consider the stability of ov-bases under
small perturbations. We generalize a result of Paley-Wiener  to the situation of ov-basis.