Some classes of matrix transforms of summability domains of normal matrices

Aasm, Ants

doi:10.2298/fil1205023a

Cited by 3 publications

(3 citation statements)

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“…In this paper we continue the studies started in [1], [2], [5], [9] and [10]. We prove necessary and sufficient conditions for…”

Section: Introductionmentioning

confidence: 72%

“…In this paper, we continued the investigations started in [1], [2], [5], [9] and [10] (see also [6]), where we studied the matrix transformations of subspaces of summability domains of matrices with real or complex entries defined by speeds of convergence, i.e. ; by monotonically increasing positive sequences λ and µ.…”

Section: Discussionmentioning

confidence: 95%

“…In this section we characterize the sets c λ A , l µ B and (c 0 ) λ A , l µ B , if A is a λreversible matrix. For the beginning we present necessary and sufficient conditions for existence of the transformation y = M x for every x ∈ (c 0 ) λ A (first proved in [2]) and for every x ∈ c λ A . Proof.…”

Section: Relation (36) Holds For Every X ∈ M λmentioning

confidence: 99%

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Matrix Transforms of Speed-Summable and Speed-Bounded Sequences

Aasma,

Natarajan

2023

FU Math Inform

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First we recall the notions of $A^{\lambda}$-boundedness, $A^{\lambda}$-summability and the absolute $A^{\lambda}$-summability of sequences, and the notion of $\lambda$-reversibility of $A$, where $A$ is a matrix with real or complex entries and $\lambda$ is the speed of convergence, \ie; a monotonically increasing positive sequence. Let $B$ be a lower triangular matrix with real or complex entries, and $\mu=(\mu_{n})$ be another speed of convergence. We find necessary and sufficient conditions for a matrix $M$ (with real or complex entries) to map the set of all $A^{\lambda}$-bounded sequences (for a normal matrix $A$) into the set of all absolutely $B^{\mu}$-summable sequences, and the set of all $A^{\lambda}$-summable sequences (for a $\lambda$-reversible matrix $A$) into the set of all absolutely $B^{\mu}$-summable sequences.

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“…In this paper we continue the studies started in [1], [2], [5], [9] and [10]. We prove necessary and sufficient conditions for…”

Section: Introductionmentioning

confidence: 72%