Zobrazeno 1 - 10
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pro vyhledávání: '"Drnovšek, Roman"'
Autor:
Drnovšek, Roman
Publikováno v:
Linear and Multilinear Algebra, 2024, 1--6
Let $T$ be an operator on Banach space $X$ that is similar to $- T$ via an involution $U$. Then $U$ decomposes the Banach space $X$ as $X = X_1 \oplus X_2$ with respect to which decomposition we have $U = \left(\begin{matrix} I_1 & 0 \\ 0 & -I_2 \end
Externí odkaz:
http://arxiv.org/abs/2311.16724
Autor:
Drnovšek, Roman, Kandić, Marko
Let $a$ and $b$ be elements of an ordered normed algebra $\mathcal A$ with unit $e$. Suppose that the element $a$ is positive and that for some $\varepsilon>0$ there exists an element $x\in \mathcal A$ with $\|x\|\leq \varepsilon$ such that $$ ab-ba
Externí odkaz:
http://arxiv.org/abs/2311.05329
Autor:
Drnovšek, Roman, Kandić, Marko
This paper extends the well-known Ringrose theory for compact operators to polynomially Riesz operators on Banach spaces. The particular case of an ideal-triangularizable Riesz operator on an order continuous Banach lattice yields that the spectrum o
Externí odkaz:
http://arxiv.org/abs/2212.10243
Autor:
Drnovšek, Roman
Let $D$ be an invertible multiplication operator on $L^2(X, \mu)$, and let $A$ be a bounded operator on $L^2(X, \mu)$. In this note we prove that $\|A\|^2 \le \|D A\| \, \|D^{-1} A\|$, where $\|\cdot\|$ denotes the operator norm. If, in addition, the
Externí odkaz:
http://arxiv.org/abs/1905.08009
Autor:
Drnovšek, Roman
Publikováno v:
Linear Algebra and its Applications 574 (2019), 40-45
In 1992, Szyld provided a sequence of lower bounds for the spectral radius of a nonnegative matrix $A$, based on the geometric symmetrization of powers of $A$. In 1998, Ta\c{s}\c{c}i and Kirkland proved a companion result by giving a sequence of uppe
Externí odkaz:
http://arxiv.org/abs/1904.01835
Autor:
Drnovšek, Roman
We prove that the inequality $$\cosh \left( \mathrm{arcosh}(2 \cosh u) \cdot \tanh u \right) < \exp \left( u \cdot \tanh u \right)$$ holds for all $u > 0$. We check with the computation program Mathematica that the ratio between the left-hand and the
Externí odkaz:
http://arxiv.org/abs/1809.08974
Autor:
Drnovšek, Roman
We give an example of a positive element $a$ in some ordered Banach algebra $A$ such that its spectrum is equal to $\{1\}$ and it is not greater than or equal to the unit element of $A$.
Comment: 3 pages
Comment: 3 pages
Externí odkaz:
http://arxiv.org/abs/1803.10942
Autor:
Drnovšek, Roman
We give short proofs of two \v{S}emrl's descriptions of order automorphisms of the effect algebra. This sheds new light on both formulas that look quite complicated. Our proofs rely on Moln\'{a}r's characterization of order automorphisms of the cone
Externí odkaz:
http://arxiv.org/abs/1803.00762
Autor:
Drnovšek, Roman
Publikováno v:
Positivity 2018
We study algebras generated by positive matrices, i.e., matrices with nonnegative entries. Some of our results hold in more general setting of vector lattices. We reprove and extend some theorems that have been recently shown by Kandi\'{c} and \v{S}i
Externí odkaz:
http://arxiv.org/abs/1710.08703
Autor:
Drnovšek, Roman, Kandić, Marko
It is known that a positive commutator $C=A B - B A$ between positive operators on a Banach lattice is quasinilpotent whenever at least one of $A$ and $B$ is compact. In this paper we study the question under which conditions a positive operator can
Externí odkaz:
http://arxiv.org/abs/1707.00882