If a modal logic L is finitely axiomatisable, then it is of course decidable whether a finite frame is a frame for L: one just has to check the finitely many axioms in it. If L is not finitely axiomatisable, then this might not be the case. For example, it is shown in [7] that the finite frame problem is undecidable for every L between the product logics K ×K ×K and S5 × S5 × S5. Here we show t...

Partial frames provide a rich context in which to do pointfree structured and unstructured topology. A small collection of axioms of an elementary nature allows one to do much traditional pointfree topology, both on the level of frames or locales, and that of uniform or metric frames. These axioms are sufficiently general to include as examples bounded distributive...

In this paper, we define super Hilbert module and investigate frames in this space. Super Hilbert modules are  generalization of super Hilbert spaces in Hilbert C*-module setting. Also, we define frames in a super Hilbert module and characterize them by using of the concept of g-frames in a Hilbert C*-module. Finally, disjoint frames in Hilbert C*-modules are introduced and investigated.

Fusion frames are a generalized form of frames in Hilbert spaces. In the present paper we introduce Bessel subfusion sequences and subfusion frames and we investigate the relationship between their operation. Also, the definition of the orthogonal complement of subfusion frames and the definition of the completion of Bessel fusion sequences are provided and several results related with these no...

When an individual’s preferences depend on the time or ‘frame’ at which decisions are made, the preferences that appear at different frames must be aggregated in order to make social decisions. Suppose we aggregate each individual i’s frame-based preferences with a ‘behavioral welfare relation’ that ranks x above y if, when both x and y are available, i sometimes choose x and not y and never ch...

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*...

Two Bessel sequences are orthogonal if the composition of the synthesis operator of one sequence with the analysis operator of the other sequence is the 0 operator. We characterize when two Bessel sequences are orthogonal when the Bessel sequences have the form of translates of a finite number of functions in L(R). The characterizations are applied to Bessel sequences which have an affine struc...

Frames in Hilbert bimodules are a special case of frames in Hilbert C*-modules. The paper considers A-frames and B-frames and their relationship in a Hilbert A-B-imprimitivity bimodule. Also, it is given that every frame in Hilbert spaces or Hilbert C*-modules is a semi-tight frame. A relation between A-frames and K(H_B)-frames is obtained in a Hilbert A-B-imprimitivity bimodule. Moreover, the ...

Frames which can be generated by the action of some operators (e.g. translation, dilation, modulation, ...) on a single element $f$ in a Hilbert space, called coherent frames. In this paper, we introduce a class of continuous frames in a Hilbert space $mathcal{H}$ which is indexed by some locally compact group $G$, equipped with its left Haar measure. These frames are obtained as the orbits of ...