Some classes of ideal convergent sequences and generalized difference matrix operator

S.A. Mohiuddine; B. Hazarika

doi:10.2298/fil1706827m

Some classes of ideal convergent sequences and generalized difference matrix operator

Filomat ◽

10.2298/fil1706827m ◽

2017 ◽

Vol 31 (6) ◽

pp. 1827-1834 ◽

Cited By ~ 14

Author(s):

S.A. Mohiuddine ◽

B. Hazarika

Keyword(s):

Matrix Operator ◽

Difference Matrix ◽

Convergent Sequences

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On the Fine Spectrum of the Operator Defined by the Lambda Matrix over the Spaces of Null and Convergent Sequences

Abstract and Applied Analysis ◽

10.1155/2013/687393 ◽

2013 ◽

Vol 2013 ◽

pp. 1-13 ◽

Cited By ~ 5

Author(s):

Medine Yeşilkayagil ◽

Feyzi Başar

Keyword(s):

Point Spectrum ◽

Sequence Spaces ◽

Matrix Operator ◽

Regular Matrix ◽

Approximate Point Spectrum ◽

Fine Spectrum ◽

New Development ◽

The Matrix ◽

Convergent Sequences

The main purpose of this paper is to determine the fine spectrum with respect to Goldberg's classification of the operator defined by the lambda matrix over the sequence spaces andc. As a new development, we give the approximate point spectrum, defect spectrum, and compression spectrum of the matrix operator on the sequence spaces andc. Finally, we present a Mercerian theorem. Since the matrix is reduced to a regular matrix depending on the choice of the sequence having certain properties and its spectrum is firstly investigated, our work is new and the results are comprehensive.

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On Zweier generalized difference ideal convergent sequences in a locally convex space defined by Musielak-Orlicz function

Boletim da Sociedade Paranaense de Matemática ◽

10.5269/bspm.v35i2.29077 ◽

2017 ◽

Vol 35 (2) ◽

pp. 19 ◽

Cited By ~ 3

Author(s):

Bipan Hazarika ◽

Karan Tamanag

Keyword(s):

Orlicz Function ◽

Convergent Sequence ◽

Locally Convex Space ◽

Sequence Spaces ◽

Infinite Matrix ◽

Difference Matrix ◽

New Class ◽

Algebraic Properties ◽

Locally Convex ◽

Convergent Sequences

Let $\mathbf{M}=(M_k)$ be a Musielak-Orlicz function. In this article, we introduce a new class of ideal convergent sequence spaces defined by Musielak-Orlicz function, using an infinite matrix, and a generalized difference matrix operator $B_{(i)}^{p}$ in locally convex spaces. We investigate some linear topological structures and algebraic properties of these spaces. We obtainsome relations related to these sequence spaces.

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