9 citations · 34 across the 12 of their papers we have counts for
17 papers
Almost multiplicative maps with respect to almost associative operations on Banach algebras
Tomasz Kochanek
We prove an Ulam type stability result for a non-associative version of the multiplicativity equation, that is, , where is a unital bounded operator acting…
Compact perturbations of operator semigroups
Tomasz Kochanek
We study lifting problems for operator semigroups in the Calkin algebra , our approach being mainly based on the Brown--Douglas--Fillmore theory. With any…
Approximately order zero maps between C*-algebras
Tomasz Kochanek
We investigate linear operators between C-algebras which approximately preserve involution and orthogonality, the latter meaning that for some we have $\|ϕ(x…
Approximate homomorphisms on lattices
Roman Badora, Tomasz Kochanek, Barbara Przebieracz
We prove two results concerning an Ulam-type stability problem for homomorphisms between lattices. One of them involves estimates by quite general error functions; the other deals…
Operator ideals and three-space properties of asymptotic ideal seminorms
Ryan M. Causey, Szymon Draga, Tomasz Kochanek
We introduce asymptotic analogues of the Rademacher and martingale type and cotype of Banach spaces and operators acting on them. Some classical local theory results related, for e…
Lipschitz-free spaces over compact subsets of superreflexive spaces are weakly sequentially complete
Tomasz Kochanek, Eva Pernecká
Let be a compact subset of a superreflexive Banach space. We prove that the Lipschitz-free space , the predual of the Banach space of Lipschitz functions on …
The Szlenk power type and tensor products of Banach spaces
Szymon Draga, Tomasz Kochanek
We prove a formula for the Szlenk power type of the injective tensor product of Banach spaces with Szlenk index at most . We also show that the Szlenk power type as well as summ…
Direct sums and summability of the Szlenk index
Szymon Draga, Tomasz Kochanek
We prove that the -sum of separable Banach spaces with uniformly summable Szlenk index has summable Szlenk index, whereas this result is no longer valid for more general direc…
Uncountable sets of unit vectors that are separated by more than 1
Tomasz Kania, Tomasz Kochanek
Let be a Banach space. We study the circumstances under which there exists an uncountable set of unit vectors such that for distinct $x,y\in \…
Steinhaus' lattice-point problem for Banach spaces
Tomasz Kania, Tomasz Kochanek
Steinhaus proved that given a~positive integer , one may find a circle surrounding exactly points of the integer lattice. This statement has been recently extended to Hilber…
A chain condition for operators from C(K)-spaces
Klaas Pieter Hart, Tomasz Kania, Tomasz Kochanek
We introduce a chain condition (bishop), defined for operators acting on C(K)-spaces, which is intermediate between weak compactness and having weakly compactly generated range. It…
Characterisation of -norms via Hölder's inequality
Tomasz Kochanek, Michał Lewicki
We characterise -norms on the space of integrable step functions, defined on a probabilistic space, via Hölder's type inequality with an optimality condition.
Almost orthogonally additive functions
Tomasz Kochanek, Wirginia Wyrobek-Kochanek
If a function , acting on a Euclidean space , is "almost" orthogonally additive in the sense that for all , where i…
Maximal left ideals of the Banach algebra of bounded operators on a Banach space
H. G. Dales, Tomasz Kania, Tomasz Kochanek +2
We address the following two questions regarding the maximal left ideals of the Banach algebra of bounded operators acting on an infinite-dimensional Banach pace $…
Stability of vector measures and twisted sums of Banach spaces
Tomasz Kochanek
A Banach space is said to have the (stability of vector measures) property if there exists a constant such that for any algebra of sets ,…
-bases with brackets and with individual brackets in Banach spaces
Tomasz Kochanek
We provide a partial answer to the question of Vladimir Kadets whether given an -basis of a Banach space , with respect to some filter $\mathcal F\subset \mathcal P(…
The ideal of weakly compactly generated operators acting on a Banach space
Tomasz Kania, Tomasz Kochanek
We call a bounded linear operator acting between Banach spaces weakly compactly generated ( for short) if its range is contained in a weakly compactly generated subsp…