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A subclass of boundary measures and the convex combination problem for Herglotz–Nevanlinna functions in several variables
Springer Science and Business Media LLC - Tập 85 - Trang 441-472 - 2019
In this paper, we begin by investigating a particular subclass of boundary
measures of Herglotz-Nevanlinna functions in two variables. Based on this, we
then proceed to solve the convex combination problem for Herglotz-Nevanlinna
functions in several variables.
Completely bounded kernels
Springer Science and Business Media LLC - Tập 79 - Trang 191-217 - 2013
We introduce completely bounded kernels taking values in $$\mathcal{L(A,B)}$$
where $$\mathcal{A}$$ and $$\mathcal{B}$$ are C*-algebras. We show that if
$$\mathcal{B}$$ is injective such kernels have a Kolmogorov decomposition
precisely when they can be scaled to be completely contractive, and that this is
automatic when the index set is countable....
Wold-type decomposition for bi-regular operators
Springer Science and Business Media LLC - Tập 87 - Trang 463-483 - 2021
We show in this paper that a Wold-type decomposition holds for the class of
regular operators with regular Moore–Penrose inverse. We also give several
examples and investigate various properties of such class of operators.
On the convergence of double integrals and a generalized version of Fubini’s theorem on successive integration
Springer Science and Business Media LLC - Tập 78 - Trang 469-487 - 2012
Let the function $$f: \overline {\mathbb{R}}_+^2 \rightarrow \mathbb{C}$$ be
such that $$f \in L_{loc}^1(\overline{\mathbb{R}}_+^2)$$ . We investigate the
convergence behavior of the double integral $$(*) \;\;\;\;\;\;\;\;\;\;\;
\int_{0}^{A} \int_{0}^{B} f(u, v)dudv \;\;\; as \;\; A,B \rightarrow \infty$$
where A and B tend to infinity independently of one another, while using two
notions of conver...
Bernstein inequality in Lα norms
Springer Science and Business Media LLC - Tập 79 - Trang 129-174 - 2013
The classical Bernstein inequality estimates the derivative of a polynomial at a
fixed point with the supremum norm and a factor depending on the point only.
Recently, this classical inequality was generalized to arbitrary compact subsets
on the real line. That generalization is sharp and naturally introduces
potential theoretical quantities. It also gives a hint how a sharp Lα Bernstein
inequalit...
$${\mathcal {C}}_1$$ -diagrams of slim rectangular semimodular lattices permit quotient diagrams
Springer Science and Business Media LLC - - Trang 1-40
Slim semimodular lattices (for short, SPS lattices) and slim rectangular
lattices (for short, SR lattices) were introduced by Grätzer and Knapp (Acta Sci
Math (Szeged) 73:445–462, 2007; 75:29–48, 2009). These lattices are necessarily
finite and planar, and they have been studied in more then four dozen papers
since 2007. They are best understood with the help of their $${\mathcal {C}}_1$$
-diagram...
Poisson summation for functions of bounded variation on ℝd
Springer Science and Business Media LLC - Tập 80 - Trang 491-498 - 2014
A one-dimensional version of the Poisson summation formula for functions of
bounded variation due to R.M. Trigub is extended to the multivariate case under
minimal assumptions on functions.
Spectral calculations on locally convex vector spaces. I
Springer Science and Business Media LLC - Tập 78 - Trang 643-667 - 2012
We develop a holomorphic functional calculus for multivalued linear operators on
locally convex vector spaces, based on the resolvent identity. This includes the
case of fractional powers along Lipschitz curves.
Isomorphic vector-valued Banach-Stone theorems for subspaces
Springer Science and Business Media LLC - Tập 81 - Trang 189-214 - 2015
Given a Banach space X, we define the number λ0(X) = inf d(X2, ℓ1(2)), where the
infimum is taken over all two-dimensional subspaces X2 of X. Here, d(M, N) means
the Banach-Mazur distance between Banach spaces M, N defined by d(M, N) =
inf{‖T‖ ‖T-1‖ : T: M → N is an isomorphism}. We establish some facts about λ0
and then consider applications to Banach-Stone type theorems for isomorphisms on
conti...
Some results on matrix transformation and compactness for fibonomial sequence spaces
Springer Science and Business Media LLC - Tập 89 - Trang 593-609 - 2023
In this paper, we introduce the Fibonomial sequence spaces $$b_{0}^{r,s,F}$$ and
$$b_{c}^{r,s,F}$$ and show that these are linearly isomorphic to the spaces
$$c_{0}$$ and c, respectively. In addition, we present $$\alpha -$$ dual,
$$\beta -$$ dual and $$\gamma -$$ dual for those spaces and characterize certain
matrix classes. In the final section, we obtain some criteria for the
compactness of ce...
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