Corrigendum on the paper Remarks on compact operators between interpolation spaces associated to polygons.
Here are given the figures of this paper, initially published with some omissions.
Corrigendum to “Commutators on ” (Studia Math. 206 (2011), 175-190)
We give a corrected proof of Theorem 2.10 in our paper “Commutators on ” [Studia Math. 206 (2011), 175-190] for the case 1 < q < p < ∞. The case when 1 = q < p < ∞ remains open. As a consequence, the Main Theorem and Corollary 2.17 in that paper are only valid for 1 < p,q < ∞.
Corrigendum to Spaces of Vector-Valued Measurable Functions.
Corrigendum to “Spectral analysis for rank one perturbations of diagonal operators in non-archimedean Hilbert space”
Corrigendum to "The Existence and Unicity of Best Approximations".
Corrigendum to "The Moment Problem in the Space C...(S)''.
Corrigendum to the paper "On the reproducing kernel for harmonic functions and the space of Bloch harmonic functions on the unit ball in R^{n}" (Studia Mathematica 87 (1987), 23-32)
Corrigendum to the paper “The universal Banach space with a -suppression unconditional basis”
We observe that the notion of an almost -universal based Banach space, introduced in our earlier paper [1]: Banakh T., Garbulińska-Wegrzyn J., The universal Banach space with a -suppression unconditional basis, Comment. Math. Univ. Carolin. 59 (2018), no. 2, 195–206, is vacuous for . Taking into account this discovery, we reformulate Theorem 5.2 from [1] in order to guarantee that the main results of [1] remain valid.
Cotype and absolutely summing homogeneous polynomials in spaces
We lift to homogeneous polynomials and multilinear mappings a linear result due to Lindenstrauss and Pełczyński for absolutely summing operators. We explore the notion of cotype to obtain stronger results and provide various examples of situations in which the space of absolutely summing homogeneous polynomials is different from the whole space of homogeneous polynomials. Among other consequences, these results enable us to obtain answers to some open questions about absolutely summing homogeneous...
Cotype and complemented copies of in spaces of operators
Cotype and (q, 1)-summing norm in a Banach space.
Cotype for p-Banach spaces
Cotype of operators from C(K).
Countable products of spaces of finite sets
We consider the compact spaces σₙ(Γ) of subsets of Γ of cardinality at most n and their countable products. We give a complete classification of their Banach spaces of continuous functions and a partial topological classification.
Countable sets of holomorphic mappings
Countable tightness in the spaces of regular probability measures
We prove that if K is a compact space and the space P(K × K) of regular probability measures on K × K has countable tightness in its weak* topology, then L₁(μ) is separable for every μ ∈ P(K). It has been known that such a result is a consequence of Martin's axiom MA(ω₁). Our theorem has several consequences; in particular, it generalizes a theorem due to Bourgain and Todorčević on measures on Rosenthal compacta.
Countably convex sets
We investigate countably convex subsets of Banach spaces. A subset of a linear space is countably convex if it can be represented as a countable union of convex sets. A known sufficient condition for countable convexity of an arbitrary subset of a separable normed space is that it does not contain a semi-clique [9]. A semi-clique in a set S is a subset P ⊆ S so that for every x ∈ P and open neighborhood u of x there exists a finite set X ⊆ P ∩ u such that conv(X) ⊈ S. For closed sets this condition...
Countably determined locally convex spaces
Countably evaluating homomorphisms on real function algebras
By studying algebra homomorphisms, which act as point evaluations on each countable subset, we obtain improved results on the question when all algebra homomorphisms are point evaluations.
Counterexample on semiradial Banach algebras