توپولوژی روی قاب ها در فضاهای هیلبرت و باناخ

let h be a separable hilbert space and let b be the set of bessel sequences in h. by using several interesting results in operator theory we study some topological properties of frames and riesz bases by constructing a banach space structure on b. the convergence of a sequence of elements in b is de_ned and we determine whether important properties of the sequence is preserved under the convergence. we give a c*-algebra structure to b and we study multiplication and adjoint of frames. an important result in operator theory helps us to write a bessel sequence as a multiple of a sum of arbitrary _nite number of orthonormal bases for h. some characterization of riesz bases and classi_cation of frames with respect to frame operators and positive operators are studied. also we study frames for tensor product of hilbert and banach spaces.