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Characterizations of compact operators on ℓp-type fractional sets of sequences

Özger Faruk

Demonstratio Mathematica

2019

Vol. 52, nr 1

105--115

Among the sets of sequences studied, difference sets of sequences are probably the most common type of sets. This paper considers some ℓp-type fractional difference sets via the gamma function. Although, we characterize compactness conditions on those sets using the main key of Hausdorff measure of noncompactness, we can only obtain sufficient conditions when the final space is ℓ∞. However, we use some recent results to exactly characterize the classes of compact matrix operators when the final space is the set of bounded sequences.

Concrete minimal 3 x 3 Hermitian matrices and some general cases

Klobouk A. H., Varela A.

Demonstratio Mathematica

2017

Vol. 50, nr 1

330--350

Given a Hermitian matrix M ∈ M₃ (ℂ) we describe explicitly the real diagonal matrices Dм such that ║M + Dм║ ≤ ║M + D║ for all real diagonal matrices D ∈ M3(ℂ), where ║ · ║ denotes the operator norm. Moreover, we generalize our techniques to some n × n cases.

On norm of single layer potentials on segments

Zoalroshd S. M.

Journal of Applied Analysis

2016

Vol. 22, nr 1

91--94

We show that, for a special case, equality of the spectra of single layer potentials defined on two segments implies that these segments must have equal length. We also provide an upper bound for the operator norm and exact expression for the Hilbert–Schmidt norm of single layer potentials on segments.