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
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...
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
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
For two commutative idempotents $$\Pi _1$$ and $$\Pi _2$$ , $$\Pi _1+\Pi _2-\Pi
_1\Pi _2$$ is clearly idempotent. By studying the characterisation of two
idempotents generated from factorizations of idempotent operator, we give a
necessary and sufficient condition for when there is no another idempotent
operator $$\Pi _3$$ which has the same range with $$\Pi _1\Pi _2$$ such that
$$\Pi _1+\Pi _2-\P...
Refinement of triangle inequality for the Schatten $$p$$-norm
Advances in Operator Theory - Tập 5 Số 4 - Trang 1635-1645 - 2020
Estimation of upper bounds of certain matrix operators on Binomial weighted sequence spaces
Advances in Operator Theory - - 2020
Estimates of the best approximations of the functions of the Nikol’skii–Besov class in the generalized space of Lorentz
Advances in Operator Theory - Tập 6 - Trang 1-36 - 2020
In this paper, we consider the generalized Lorentz space of periodic functions
of several variables and the Nikol’skii–Besov space of functions. The article
establishes a sufficient condition for a function to belong from one generalized
Lorentz space to another space in terms of the difference of the partial sums of
the Fourier series of a given function. Exact in order estimates of the best
appr...
Existence of a solution to a nonlocal Schrödinger system problem in fractional modular spaces
Advances in Operator Theory - - 2022
Isomorphisms of $$AC(\sigma )$$ spaces for linear graphs
Advances in Operator Theory - Tập 5 Số 2 - Trang 474-488 - 2020
We show that among compact subsets of the plane which are drawings of linear
graphs, two sets $$\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 )$$...
Two classes of operators related to the perturbation classes problem
Advances in Operator Theory - - 2023
AbstractLet $${{\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 {\mat...
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