Compact operators on the Jordan totient sequence spaces

İlkhan, Merve; Kara, Emrah Evren; Usta, Fuat

doi:10.1002/mma.6537

Cited by 14 publications

(3 citation statements)

References 19 publications

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“…For relevant literature, one may refer to [2,13,40,[49][50][51][52]. The reader may also consult the recent publications [22,24,25,53,62], which are related to compact operators and Hmnc in BK -spaces.…”

Section: Hausdorff Measure Of Non-compactness (Hmnc)mentioning

confidence: 99%

Sequence spaces derived by the triple band generalized Fibonacci difference operator

Yaying¹,

Hazarika

Mohiuddine

et al. 2020

Adv Differ Equ

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In this article we introduce the generalized Fibonacci difference operator $\mathsf{F}(\mathsf{B})$ F ( B ) by the composition of a Fibonacci band matrix and a triple band matrix $\mathsf{B}(x,y,z)$ B ( x , y , z ) and study the spaces $\ell _{k}( \mathsf{F}(\mathsf{B}))$ ℓ k ( F ( B ) ) and $\ell _{\infty }(\mathsf{F}(\mathsf{B}))$ ℓ ∞ ( F ( B ) ) . We exhibit certain topological properties, construct a Schauder basis and determine the Köthe–Toeplitz duals of the new spaces. Furthermore, we characterize certain classes of matrix mappings from the spaces $\ell _{k}(\mathsf{F}(\mathsf{B}))$ ℓ k ( F ( B ) ) and $\ell _{\infty }(\mathsf{F}(\mathsf{B}))$ ℓ ∞ ( F ( B ) ) to space $\mathsf{Y}\in \{\ell _{\infty },c_{0},c,\ell _{1},cs_{0},cs,bs\}$ Y ∈ { ℓ ∞ , c 0 , c , ℓ 1 , c s 0 , c s , b s } and obtain the necessary and sufficient condition for a matrix operator to be compact from the spaces $\ell _{k}(\mathsf{F}(\mathsf{B}))$ ℓ k ( F ( B ) ) and $\ell _{\infty }(\mathsf{F}(\mathsf{B}))$ ℓ ∞ ( F ( B ) ) to $\mathsf{Y}\in \{ \ell _{\infty }, c, c_{0}, \ell _{1},cs_{0},cs,bs\} $ Y ∈ { ℓ ∞ , c , c 0 , ℓ 1 , c s 0 , c s , b s } using the Hausdorff measure of non-compactness.

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Section: Hausdorff Measure Of Non-compactness (Hmnc)mentioning

confidence: 99%

Sequence spaces derived by the triple band generalized Fibonacci difference operator

Yaying¹,

Hazarika

Mohiuddine

et al. 2020

Adv Differ Equ

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“…Also, in [29], new Banach spaces are obtained by the aid of matrix domain of this matrix in the spaces ∞ , c, c 0 . In [30], the authors have studied the compact operators on the resulting spaces. The Riesz matrix E = (e i j ) is defined as…”

Section: Introductionmentioning

confidence: 99%

New Banach Sequence Spaces Defined by Jordan Totient Function

DEVLETLİ,

ILKHAN KARA

2023

Communications in Advanced Mathematical Sciences

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“…Tribonacci [49,50], and some special functions [22,26,[28][29][30]. Moreover, various remarkable topologic properties including almost convergence and core theorems, special duals, Hausdorff measure of noncompactness, matrix mappings, etc.…”

Section: Introductionmentioning

confidence: 99%

Certain topological properties for almost convergent Catalan-Motzkin sequence space

DAĞLI

2023

Hacettepe Journal of Mathematics and Statistics

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The purpose of this paper is to introduce a new almost convergent sequence space by means of a matrix involving Catalan and Motzkin numbers. It is demonstrated that this novel sequence space and the space of all almost convergent sequences are linearly isomorphic and the beta- dual of this new space is deduced. In addition, by defining Catalan-Motzkin core of a complex-valued sequence, certain inclusion relations are derived for it.

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Compact operators on the Jordan totient sequence spaces

Cited by 14 publications

References 19 publications

Sequence spaces derived by the triple band generalized Fibonacci difference operator

Sequence spaces derived by the triple band generalized Fibonacci difference operator

New Banach Sequence Spaces Defined by Jordan Totient Function

Certain topological properties for almost convergent Catalan-Motzkin sequence space

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