in this paper, we show that in each nite dimensional hilbert space, a frame of subspaces is an ultra bessel sequence of subspaces. we also show that every frame of subspaces in a nite dimensional hilbert space has frameness bound.

and Applied Analysis 3 2. ap Δ Difference Sequence Space In the present section, we introduce the difference sequence space ap Δ and emphasize its some properties. Although the difference sequence space λ Δ corresponding to the space λ was defined by Kızmaz 10 as follows: λ Δ {x xk ∈ ω : xk − xk 1 ∈ λ}, 2.1 the difference sequence space corresponding to the space p was not examined, where λ den...

The idea of difference sequence spaces were introduced by Kizmaz [6] and generalized by Et. and Colak [4]. Later Tripathy, Esi and Tripathy [15] introduced the notion of the new difference operator ∆m for n,m ∈ N . In this paper we introduced some new type of generalized difference sequence spaces defined by a modulus function and the new type of statistically convergent generalized difference ...

In this paper, we show that in each nite dimensional Hilbert space, a frame of subspaces is an ultra Bessel sequence of subspaces. We also show that every frame of subspaces in a nite dimensional Hilbert space has frameness bound.

in this paper we introduce entire sequence spaces defined by a sequence of modulus functions . we study some topological properties of these spaces and prove some inclusion relations.

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