Geodesic
Matrix transforms between sequence spaces defined by speeds of convergence
Filomat, Tome 37 (2023) no. 4, p. 1029

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DOI

Let X, Y be two sequence spaces defined by speeds of the convergence, i.e.; by monotonically increasing positive sequences. In this paper, we give necessary and sufficient conditions for a matrix A (with real or complex entries) to map X into Y. Also the analogue of the well known result of Steinhaus, which states that a regular matrix cannot transform each bounded sequence into convergent sequence, for the sequence spaces defined by the speeds of convergence has been proved.
DOI : 10.2298/FIL2304029A
Classification : 40C05, 40D05, 41A25
Keywords: Matrix transforms, convergence and boundedness with speed, λ-conservative, τ-multiplicative, λ-regular 
Ants Aasma; P N Natarajan. Matrix transforms between sequence spaces defined by speeds of convergence. Filomat, Tome 37 (2023) no. 4, p. 1029 . doi: 10.2298/FIL2304029A
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     title = {Matrix transforms between sequence spaces defined by speeds of convergence},
     journal = {Filomat},
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     year = {2023},
     volume = {37},
     number = {4},
     doi = {10.2298/FIL2304029A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2304029A/}
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