9 citations · 38 across the 24 of their papers we have counts for
26 papers
Extensive approach to absolute homogeneity
Piotr Niemiec
The main aim of the paper is to study in greater detail absolutely homogeneous structures (that is, objects with the property that each partial isomorphism extends to a global auto…
Positive Hankel operators, positive definite kernels and related topics
Piotr Niemiec
It is shown that a positive (bounded linear) operator on a Hilbert space with trivial kernel is unitarily equivalent to a Hankel operator that satisfies double positivity condition…
A note on functions preserving positive definiteness
Piotr Niemiec
The aim of the paper is to give a full characterization of functions f from I into the real line R (where I is an interval in R that satisfies certain natural conditions) such that…
Hyperbolic geometry for non-differential topologists
Piotr Niemiec, Piotr Pikul
A soft presentation of hyperbolic spaces, free of differential apparatus, is offered. Fifth Euclid's postulate in such spaces is overthrown and, among other things, it is proved th…
Applications of amenable semigroups in operator theory
Piotr Niemiec, Paweł Wójcik
The paper deals with continuous homomorphisms of amenable semigroups into the algebra of all bounded linear operators on a Banach space $E…
Functional calculus in finite type I von Neumann algebras
Piotr Niemiec
A certain class of matrix-valued Borel matrix functions is introduced and it is shown that all functions of that class naturally operate on any operator T in a finite type I von Ne…
Models for subhomogeneous C*-algebras
Piotr Niemiec
A new category of topological spaces with additional structures, called m-towers, is introduced. It is shown that there is a covariant functor which establishes a one-to-one corres…
Applications of Ultrafilters in Ergodic Theory and Combinatorial Number Theory
Jakub Konieczny
Ultrafilters are very useful and versatile objects with applications throughout mathematics: in topology, analysis, combinarotics, model theory, and even theory of social choice. P…
Bounded convergence theorems
Piotr Niemiec
There are presented certain results on extending continuous linear operators defined on spaces of E-valued continuous functions (defined on a compact Hausdorff space X) to linear o…
Direct integrals of matrices
Piotr Niemiec
It is shown that each linear operator on a separable Hilbert space which generates a finite type I von Neumann algebra has, up to unitary equivalence, a unique representation as a…
Algebra of operators affiliated with a finite type I von Neumann algebra
Piotr Niemiec, Adam Wegert
It is shown that the *-algebra of all (closed densely defined linear) operators affiliated with a finite type I von Neumann algebra admits a unique center-valued trace, which turns…
Functional calculus for diagonalizable matrices
Piotr Niemiec
For an arbitrary function f:Ω\rightarrow C (where Ωis a subset of the field C) and a positive integer k let f act on all diagonalizable complex matrices whose all eigenvalues lie i…
Elementary approach to homogeneous C*-algebras
Piotr Niemiec
A C*-algebra is n-homogeneous (where n is finite) if every its nonzero irreducible representation acts on an n-dimensional Hilbert space. An elementary proof of Fell's characteriza…
Isometry groups among topological groups
Piotr Niemiec
It is shown that a topological group G is topologically isomorphic to the isometry group of a (complete) metric space iff G coincides with its G-delta-closure in the Rajkov complet…
Isometry groups of proper metric spaces
Piotr Niemiec
Given a locally compact Polish space X, a necessary and sufficient condition for a group G of homeomorphisms of X to be the full isometry group of (X,d) for some proper metric d on…
Borel structure of the spectrum of a closed operator
Piotr Niemiec
For a linear operator in a Banach space let denote the point spectrum of , for finite be the set of all such that $\dim \ker (T…
Problem with almost everywhere equality
Piotr Niemiec
A topological space is said to have (AEEP) if the following condition is fulfilled. Whenever is a measurable space and are two measurable fun…
Norm closures of orbits of bounded operators
Piotr Niemiec
To every bounded linear operator between Hilbert spaces and three cardinals , and and a binary number are assigne…
Normal systems over ANR's, rigid embeddings and nonseparable absorbing sets
Piotr Niemiec
Most of results of Bestvina and Mogilski [\textit{Characterizing certain incomplete infinite-dimensional absolute retracts}, Michigan Math. J. \textbf{33} (1986), 291--313] on stro…
Spaces of measurable functions
Piotr Niemiec
For a metrizable space and a finite measure space let and be the spaces of all equivalence classes (under the relation of equality almo…
Extending maps by injective --maps in Hilbert manifolds
Piotr Niemiec
The aim of the paper is to prove that if is a metrizable manifold modelled on a Hilbert space of dimension and is its --set, then for every completel…
Functor of continuation in Hilbert cube and Hilbert space
Piotr Niemiec
A -set in a metric space is a closed subset of such that each map of the Hilbert cube into can uniformly be approximated by maps of into .…
A note on ANR's
Piotr Niemiec
It is shown that if for a complete metric space there is a constant such that the intersection of open balls is nonempty for every fin…
Unitary equivalence and decompositions of finite systems of closed densely defined operators in Hilbert spaces
Piotr Niemiec
An \textit{ideal} of -tuples of operators is a class invariant with respect to unitary equivalence which contains direct sums of arbitrary collections of its members as well as…