Yazar "Roopaei, Hadi" seçeneğine göre listele

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    Banach Spaces and Inequalities Associated with New Generalization of Cesaro Matrix
    (Springer, 2023) Basar, Feyzi; Roopaei, Hadi
    Let the triangle matrix A(ru) be a generalization of the Cesaro matrix and U & ISIN; {c(0), c, l(& INFIN;)}. In this study, we essentially deal with the space U(A(ru)) defined by the domain of A(ru) in the space U and give the bases, and determine the Kothe-Toeplitz, generalized Kothe-Toeplitz and bounded-duals of the space U (A(ru)). We characterize the classes (l(& INFIN;) (A(ru)):l(& INFIN;)), (l(& INFIN;)(A(ru)): c), (c(A(ru)): c), and (U: V(A(ru))) of infinite matrices, where V denotes any given sequence space. Additionally, we also present a Steinhaus type theorem. As an another result of this study, we investigate the l(p)-norm of the matrix A(ru) and as a result obtaining a generalized version of Hardy's inequality, and some inclusion relations. Moreover, we compute the norm of well-known operators on the matrix domain l(p) (A(ru)).
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    On the factorable spaces of absolutely p-summable, null, convergent, and bounded sequences
    (Walter De Gruyter Gmbh, 2021) Basar, Feyzi; Roopaei, Hadi
    Let F denote the factorable matrix and X is an element of {l(p), c(0), c, l(infinity)}. In this study, we introduce the domains X(F) of the factorable matrix in the spaces X. Also, we give the bases and determine the alpha-, beta- and gamma-duals of the spaces X(F). We obtain the necessary and sufficient conditions on an infinite matrix belonging to the classes (l(p)(F), l(infinity)), (l(p)(F), f) and (X, Y(F)) of matrix transformations, where Y denotes any given sequence space. Furthermore, we give the necessary and sufficient conditions for factorizing an operator based on the matrix F and derive two factorizations for the Cesaro and Hilbert matrices based on the Gamma matrix. Additionally, we investigate the norm of operators on the domain of the matrix F. Finally, we find the norm of Hilbert operators on some sequence spaces and deal with the lower bound of operators on the domain of the factorable matrix.
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    On the Gamma Spaces Including the Spaces of Absolutely p-Summable, Null, Convergent and Bounded Sequences
    (Taylor & Francis Inc, 2022) Roopaei, Hadi; Basar, Feyzi
    In this paper, we investigate some properties of the domains l(p) (Gamma(n)), c(0) (Gamma(n)), c(Gamma(n)) and l(infinity)(Gamma(n)) of the Gamma matrix of order n in the classical spaces l(p), C-0, c and l(infinity) of absolutely p-summable, null, convergent and bounded sequences, respectively, and compute the alpha-, beta- and gamma-duals of these spaces. We characterize the classes of infinite matrices from the space l(p) (Gamma(n)) to the spaces l(infinity) and f, and from a normed sequence space to the gamma sequence spaces l(p)(Gamma(n)), c(0) (Gamma(n)), c(Gamma(n)) and l(infinity)(Gamma(n)). Moreover, we introduce the necessary and sufficient conditions for factorizing an operator based on the weighted mean matrices and derive the factorizations for the Cesaro and Hilbert matrices based on the Gamma matrix. Finally, we emphasize on the lower bound of operators from l(p) into l(p) (Gamma(n)), from l(p)(Gamma(n)) into l(p), from l(p) (Gamma(n)) into itself and from l(p) into itself.
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    On the spaces of Cesaro absolutelyp-summable, null, and convergent sequences
    (Wiley, 2021) Roopaei, Hadi; Basar, Feyzi
    In this paper, we investigate some properties of the domainsc(0)(C-n),c(C-n), andl(p)(C-n)with0 < p < 1of the Cesaro matrix of ordernin the classical spacesc(0),c, andl(p)of null, convergent, and absolutelyp-summable sequences, respectively, and compute the alpha-,beta-, and gamma-duals of these spaces. We characterize the classes of infinite matrices from the spacel(p)(C-n)to the spacesl(infinity),c, andc(0)and from a normed sequence spaces to the sequence spacesc(0)(C-n),c(C-n), andl(p)(C-n). Moreover, we compute the lower bound of operators froml(p)intol(p)(C-n), froml(p)(C-n)intol(p)and froml(p)(C-n)into itself.