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: | , |
| Format: | Journal Article |
| Language: | English |
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01.12.2024
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| ISSN: | 1425-6908, 1869-6082 |
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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 | Nezir, V.; Dutta, H.; Yıldırım, S. (j_jaa-2023-0123_ref_011) 2022; 36 Sager, N.; Sağır, B. (j_jaa-2023-0123_ref_014) 2020; 9 Sağır, B.; Değirmen, N.; Duyar, C. (j_jaa-2023-0123_ref_015) 2023; 85 Malkowsky, E. (j_jaa-2023-0123_ref_009) 1989; 46(60) Segre, C. (j_jaa-2023-0123_ref_016) 1892; 40 Dutta, H. (j_jaa-2023-0123_ref_007) 2010; 8 Malkowsky, E.; Savas, E. (j_jaa-2023-0123_ref_010) 2004; 147 Dutta, H. (j_jaa-2023-0123_ref_006) 2009; 2 Bera, S.; Tripathy, B. C. (j_jaa-2023-0123_ref_005) 2023; 12(30) Raj, K.; Esi, A.; Sharma, C. (j_jaa-2023-0123_ref_013) 2023; 37 2024112720334983454_j_jaa-2023-0123_ref_007 2024112720334983454_j_jaa-2023-0123_ref_006 2024112720334983454_j_jaa-2023-0123_ref_017 2024112720334983454_j_jaa-2023-0123_ref_009 2024112720334983454_j_jaa-2023-0123_ref_008 2024112720334983454_j_jaa-2023-0123_ref_003 2024112720334983454_j_jaa-2023-0123_ref_014 2024112720334983454_j_jaa-2023-0123_ref_002 2024112720334983454_j_jaa-2023-0123_ref_013 2024112720334983454_j_jaa-2023-0123_ref_005 2024112720334983454_j_jaa-2023-0123_ref_016 2024112720334983454_j_jaa-2023-0123_ref_004 2024112720334983454_j_jaa-2023-0123_ref_015 2024112720334983454_j_jaa-2023-0123_ref_010 2024112720334983454_j_jaa-2023-0123_ref_001 2024112720334983454_j_jaa-2023-0123_ref_012 2024112720334983454_j_jaa-2023-0123_ref_011 |
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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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