We develop a natural generalization of vector-valued frame theory, which we term operator-valued frame theory, using operator-algebraic methods. This extends work of the second author and D. Han which can be viewed as the multiplicity one case and extends to higher multiplicity their dilation approach. We prove several results for operator-valued frames concerning duality, disjointedness, compl...

In this paper, by using the sequence of adjointable operators from pro-C*-algebra $ mathcal{A} $ into a Hilbert $ mathcal{A} $-module $ E $. We introduce frames with bounds in pro-C*-algebra $ mathcal{A} $. New frames in Hilbert modules over pro-C*-algebras are called standard $ ast $-frames of multipliers. Meanwhile, we study several useful properties of standard $ ast $-frames in Hilbert modu...

Steel Plate Shear Wall (SPSW) is an emerging seismic load-resistant system that, compared to other systems, enjoys the advantages of stable ductile behavior, fewer detailing requirements, rapid constructability, and economy. American seismic provisions decree that a SPSW should be designed as a moment frame with a web infill plate. Specifically, in case of buildings taller than 160 ft, it decre...

Controlled frames have been introduced to improve the numerical efficiency of iterative algorithms for inverting the frame operator on abstract Hilbert spaces. Fusion frames and g-frames generalize frames. Hilbert C*-modules form a wide category between Hilbert spaces and Banach spaces. Hilbert C*-modules are generalizations of Hilbert spaces by allowing the inner product to take values in a C*...

This paper uses frame techniques to characterize the Schatten class properties of integral operators. The main result shows that if the coefficients {〈k,Φm,n〉} of certain frame expansions of the kernel k of an integral operator are in l, then the operator is Schatten p-class. As a corollary, we conclude that if the kernel or Kohn-Nirenberg symbol of a pseudodifferential operator lies in a parti...

Hilbert space frame theory has applications to various areas of pure mathematics, applied mathematics, and engineering. However, the question of how applying an invertible operator to a frame changes its properties has not yet been satisfactorily answered, and only partial results are known to date. In this paper, we will provide a comprehensive study of those questions, and, in particular, pro...

Let H be a Hilbert space. Given a bounded positive definite operator S on H, and a bounded sequence c = {ck}k∈N of non negative real numbers, the pair (S, c) is frame admissible, if there exists a frame {fk}k∈N on H with frame operator S, such that ‖fk‖ 2 = ck, k ∈ N. We relate the existence of such frames with the Schur-Horn theorem of majorization, and give a reformulation of the extended ver...

Spectral tetris is a flexible and elementary method to derive unit norm frames with a given frame operator having all of its eigenvalues ≥ 2. One important application of this method is to construct fusion frames. We will give necessary and sufficient conditions for a spectral tetris construction to give a fusion frame with prescribed eigenvalues for its fusion frame operator and with prescribe...