A note on Köthe–Toeplitz duals and multiplier spaces of sequence spaces involving bicomplex numbers
In this paper, we generalize the notions of the Köthe–Toeplitz duals of sequence spaces by introducing the concepts of bicomplex α-dual, bicomplex β-dual and bicomplex γ-dual, and also we compute them for some bicomplex sequence spaces for , and . Furthermore, we define a concept of bicomplex multip...
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| Published in: | Journal of applied analysis Vol. 30; no. 2; pp. 301 - 310 |
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| Main Authors: | , |
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| Language: | English |
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De Gruyter
01.12.2024
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| Abstract | In this paper, we generalize the notions of the Köthe–Toeplitz duals of
sequence spaces by introducing the concepts of bicomplex α-dual,
bicomplex β-dual and bicomplex γ-dual, and also we compute
them for some bicomplex sequence spaces
for
,
and
. Furthermore, we define a concept of bicomplex
multiplier space as the bicomplex version of multiplier space of two
sequence spaces and support this definition with examples. |
|---|---|
| AbstractList | In this paper, we generalize the notions of the Köthe–Toeplitz duals ofsequence spaces by introducing the concepts of bicomplex α-dual,bicomplex β-dual and bicomplex γ-dual, and also we computethem for some bicomplex sequence spaces lp(ð"¹ℂ)for 1≤p≤∞, c0(ð"¹ℂ) and c(ð"¹ℂ). Furthermore, we define a concept of bicomplexmultiplier space as the bicomplex version of multiplier space of twosequence spaces and support this definition with examples. In this paper, we generalize the notions of the Köthe–Toeplitz duals of sequence spaces by introducing the concepts of bicomplex α-dual, bicomplex β-dual and bicomplex γ-dual, and also we compute them for some bicomplex sequence spaces l p ( ℂ ) {l_{p}(\mathbb{BC})} for 1 ≤ p ≤ ∞ {1\leq p\leq\infty} , c 0 ( ℂ ) {c_{0}(\mathbb{BC})} and c ( ℂ ) {c(\mathbb{BC})} . Furthermore, we define a concept of bicomplex multiplier space as the bicomplex version of multiplier space of two sequence spaces and support this definition with examples. In this paper, we generalize the notions of the Köthe–Toeplitz duals of sequence spaces by introducing the concepts of bicomplex α-dual, bicomplex β-dual and bicomplex γ-dual, and also we compute them for some bicomplex sequence spaces for , and . Furthermore, we define a concept of bicomplex multiplier space as the bicomplex version of multiplier space of two sequence spaces and support this definition with examples. |
| Author | Değirmen, Nilay Sağır, Birsen |
| Author_xml | – sequence: 1 givenname: Nilay surname: Değirmen fullname: Değirmen, Nilay email: nilay.sager@omu.edu.tr organization: Department of Mathematics, Ondokuz Mayıs University, Samsun, Turkey – sequence: 2 givenname: Birsen surname: Sağır fullname: Sağır, Birsen email: bduyar@omu.edu.tr organization: Department of Mathematics, Ondokuz Mayıs University, Samsun, Turkey |
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| References_xml | – volume: 85 start-page: 115 issue: 4 year: 2023 end-page: 128 ident: j_jaa-2023-0123_ref_015 article-title: Bicomplex matrix transformations between c 0 c_{0} and c in bicomplex setting publication-title: Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. – volume: 12(30) start-page: 3 issue: 2 year: 2023 end-page: 16 ident: j_jaa-2023-0123_ref_005 article-title: Statistical bounded sequences of bi-complex numbers publication-title: Probl. Anal. Issues Anal. – volume: 2 start-page: 554 issue: 4 year: 2009 end-page: 563 ident: j_jaa-2023-0123_ref_006 article-title: On Köthe–Toeplitz and null duals of some difference sequence spaces defined by Orlicz functions publication-title: Eur. J. Pure Appl. Math. – volume: 9 start-page: 891 issue: 2 year: 2020 end-page: 902 ident: j_jaa-2023-0123_ref_014 article-title: On completeness of some bicomplex sequence spaces publication-title: Palest. J. Math. – volume: 37 start-page: 2421 issue: 8 year: 2023 end-page: 2435 ident: j_jaa-2023-0123_ref_013 article-title: Orlicz-lacunary bicomplex sequence spaces of difference operators publication-title: Filomat – volume: 40 start-page: 413 issue: 3 year: 1892 end-page: 467 ident: j_jaa-2023-0123_ref_016 article-title: Le rappresentazioni reali delle forme complesse e gli enti iperalgebrici publication-title: Math. Ann. – volume: 46(60) start-page: 97 year: 1989 end-page: 103 ident: j_jaa-2023-0123_ref_009 article-title: Absolute and ordinary Köthe–Toeplitz duals of some sets of sequences and matrix transformations publication-title: Publ. Inst. Math. (Beograd) (N. S.) – volume: 8 start-page: 11 issue: 1 year: 2010 end-page: 19 ident: j_jaa-2023-0123_ref_007 article-title: Generalized difference sequence spaces defined by Orlicz functions and their Köthe–Toeplitz and null duals publication-title: Thai J. Math. – volume: 147 start-page: 333 issue: 2 year: 2004 end-page: 345 ident: j_jaa-2023-0123_ref_010 article-title: Matrix transformations between sequence spaces of generalized weighted means publication-title: Appl. Math. Comput. – volume: 36 start-page: 5795 issue: 17 year: 2022 end-page: 5802 ident: j_jaa-2023-0123_ref_011 article-title: A large class in Köthe–Toeplitz duals of generalized Cesàro difference sequence spaces with fixed point property for nonexpansive mappings publication-title: Filomat – ident: 2024112720334983454_j_jaa-2023-0123_ref_016 doi: 10.1007/BF01443559 – ident: 2024112720334983454_j_jaa-2023-0123_ref_013 doi: 10.2298/FIL2308421R – ident: 2024112720334983454_j_jaa-2023-0123_ref_004 doi: 10.1201/9781351166928 – ident: 2024112720334983454_j_jaa-2023-0123_ref_006 – ident: 2024112720334983454_j_jaa-2023-0123_ref_007 – ident: 2024112720334983454_j_jaa-2023-0123_ref_011 doi: 10.2298/FIL2217795N – ident: 2024112720334983454_j_jaa-2023-0123_ref_002 doi: 10.1007/978-81-322-1886-9 – ident: 2024112720334983454_j_jaa-2023-0123_ref_012 – ident: 2024112720334983454_j_jaa-2023-0123_ref_009 – ident: 2024112720334983454_j_jaa-2023-0123_ref_005 doi: 10.15393/j3.art.2023.13090 – ident: 2024112720334983454_j_jaa-2023-0123_ref_017 – ident: 2024112720334983454_j_jaa-2023-0123_ref_008 doi: 10.1007/978-3-319-24868-4 – ident: 2024112720334983454_j_jaa-2023-0123_ref_015 – ident: 2024112720334983454_j_jaa-2023-0123_ref_014 – ident: 2024112720334983454_j_jaa-2023-0123_ref_001 doi: 10.1007/978-3-319-05110-9 – ident: 2024112720334983454_j_jaa-2023-0123_ref_010 doi: 10.1016/S0096-3003(02)00670-7 – ident: 2024112720334983454_j_jaa-2023-0123_ref_003 doi: 10.2174/97816080545231120101 |
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| Snippet | In this paper, we generalize the notions of the Köthe–Toeplitz duals of
sequence spaces by introducing the concepts of bicomplex α-dual,
bicomplex β-dual and... In this paper, we generalize the notions of the Köthe–Toeplitz duals ofsequence spaces by introducing the concepts of bicomplex α-dual,bicomplex β-dual and... |
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| SubjectTerms | 40A05 46A45 46B45 Bicomplex numbers multiplier space Multipliers sequence spaces |
| Title | A note on Köthe–Toeplitz duals and multiplier spaces of sequence spaces involving bicomplex numbers |
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