Advances in Operator Theory

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The metric-valued Lebesgue differentiation theorem in measure spaces and its applications
Advances in Operator Theory - - 2023
Danka Lučić, Enrico Pasqualetto
We prove a version of the Lebesgue differentiation theorem for mappings that are defined on a measure space and take values into a metric space, with respect to the differentiation basis induced by a von Neumann lifting. As a consequence, we obtain a lifting theorem for the space of sections of a measurable Banach bundle and a disintegration theorem for vector measures whose target is a Banach spa...... hiện toàn bộ
Characterizations of extra-invariant spaces under the left translations on a Lie group
Advances in Operator Theory - Tập 8 Số 3 - Trang 1-16 - 2023
Sarkar, Sudipta, Shukla, Niraj K.
In the context of a connected, simply connected nilpotent Lie group, whose representations are square-integrable modulo the center, we find characterization results of extra-invariant spaces under the left translations associated with the range functions. Consequently, the theory is valid for the Heisenberg group $${\mathbb {H}}^d,$$ a 2-step nilpotent Lie group.
Factorizations of idempotent operator as products of two idempotents
Advances in Operator Theory - Tập 8 - Trang 1-16 - 2023
Wei Luo
For two commutative idempotents $$\Pi _1$$ and $$\Pi _2$$ , $$\Pi _1+\Pi _2-\Pi _1\Pi _2$$ is c...... hiện toàn bộ
Refinement of triangle inequality for the Schatten $$p$$-norm
Advances in Operator Theory - Tập 5 Số 4 - Trang 1635-1645 - 2020
Ahmad Al-Natoor, Wasim Audeh
Estimation of upper bounds of certain matrix operators on Binomial weighted sequence spaces
Advances in Operator Theory - - 2020
Taja Yaying, Bipan Hazarika, S. A. Mohiuddine, M. Mursaleen
Estimates of the best approximations of the functions of the Nikol’skii–Besov class in the generalized space of Lorentz
Advances in Operator Theory - Tập 6 - Trang 1-36 - 2020
G. Akishev
In this paper, we consider the generalized Lorentz space of periodic functions of several variables and the Nikol’skii–Besov space of functions. The article establishes a sufficient condition for a function to belong from one generalized Lorentz space to another space in terms of the difference of the partial sums of the Fourier series of a given function. Exact in order estimates of the best appr...... hiện toàn bộ
Existence of a solution to a nonlocal Schrödinger system problem in fractional modular spaces
Advances in Operator Theory - - 2022
Hamza El-Houari, Lalla Saâdia Chadli, H. Moussa
Isomorphisms of $$AC(\sigma )$$ spaces for linear graphs
Advances in Operator Theory - Tập 5 Số 2 - Trang 474-488 - 2020
Al-shakarchi, Shaymaa, Doust, Ian
We show that among compact subsets of the plane which are drawings of linear graphs, two sets $$\sigma $$ and $$\tau $$ are homeomorphic if and only if the corresponding spaces of absolutely continuous functions (in the sense of Ashton and Doust) are isomorphic as Banach algebras. This gives an analogue for this class of sets to the well-known result of Gelfand and Kolmogorov for $$C(\varOmega )$$...... hiện toàn bộ
Operator means deformed by a fixed point method
Advances in Operator Theory - - 2020
Fumio Hiai
Two classes of operators related to the perturbation classes problem
Advances in Operator Theory - - 2023
Manuel González, Margot Salas-Brown
AbstractLet $${{\mathcal {S}}}{{\mathcal {S}}}$$ S S and $${{\mathcal {S}}}{{\mathcal {C}}}$$ S C be the strictly singular and the strictly cosingular operators acting between Banach spaces, and let $$P\Phi _+$$ P Φ + and $$P\Phi _+$$ P Φ + be the perturbation classes for the upper and the lower semi-Fredholm operators. We study two classes of operators $$\Phi {\mathcal {S}}$$ Φ S and $$\Phi {\mathcal {C}}$$ Φ C that satisfy $${{\mathcal {S}}}{{\mathcal {S}}}\subset \Phi {\mathcal {S}}\subset P\Phi _+$$ S S ⊂ Φ S ⊂ P Φ + and $${{\mathcal {S}}}{{\mathcal {C}}}\subset \Phi {\mathcal {C}}\subset P\Phi _-.$$ hiện toàn bộ
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