operator-valued bases on hilbert spaces

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 [4] to the situation of ov-basis.