Ondřej F. K. Kalenda
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View article: Order type relations on the set of tripotents in a JB∗-triple
Order type relations on the set of tripotents in a JB∗-triple Open
We introduce, investigate and compare several order type relations on the set of tripotents in a JB∗-triple. The main two relations we address are ≤h and ≤n. We write u≤he (or u≤ne) if u is a self-adjoint (or normal) element of the Peirce-…
View article: Simpliciality of vector-valued function spaces
Simpliciality of vector-valued function spaces Open
We investigate integral representation of vector-valued function spaces, i.e., of subspaces $H\subset C(K,E)$, where $K$ is a compact space and $E$ is a (real or complex) Banach space. We point out that there are two possible ways of gener…
View article: Transference of measures via disintegration
Transference of measures via disintegration Open
Given a compact space $K$ and a Banach space $E$ we study the structure of positive measures on the product space $K\times B_{E^*}$ representing functionals on $C(K,E)$, the space of $E$-valued continuous functions on $K$. Using the techni…
View article: On simpliciality of function spaces not containing constants
On simpliciality of function spaces not containing constants Open
We investigate simpliciality of function spaces without constants. We prove, in particular, that several properties characterizing simpliciality in the classical case differ in this new setting. We also show that it may happen that a given…
View article: Boundary integral representation of multipliers of fragmented affine functions and other intermediate function spaces
Boundary integral representation of multipliers of fragmented affine functions and other intermediate function spaces Open
We develop a theory of abstract intermediate function spaces on a compact convex set $X$ and study the behaviour of multipliers and centers of these spaces. In particular, we provide some criteria for coincidence of the center with the spa…
View article: Topologies related to (I)-envelopes
Topologies related to (I)-envelopes Open
We investigate the question whether the (I)-envelope of any subset of a dual to a Banach space $X$ may be described as the closed convex hull in a suitable topology. If $X$ contains no copy of $\ell^1$ then the weak topology generated by f…
View article: Determinants in Jordan matrix algebras
Determinants in Jordan matrix algebras Open
Acknowledgements The first author was supported by the project OPVVV
\nCAAS CZ.02.1.01/0.0/0.0/16 019/0000778. Third author partially supported by
\nMCIN / AEI / 10. 13039 / 501100011033 / FEDER “Una manera de hacer Europa”
\nproject no. P…
View article: On optimality of constants in the Little Grothendieck Theorem
On optimality of constants in the Little Grothendieck Theorem Open
We explore the optimality of the constants making valid the recently established Little Grothendieck inequality for JB$^*$-triples and JB$^*$-algebras. In our main result we prove that for each bounded linear operator $T$ from a JB$^*$-alg…
View article: Preduals of JBW*-triples are 1-Plichko spaces
Preduals of JBW*-triples are 1-Plichko spaces Open
We prove that the predual, $M_*$, of a JBW$^*$-triple $M$ is a 1-Plichko space (i.e. it admits a countably 1-norming Markushevich basis or, equivalently, it has a commutative 1-projectional skeleton), and obtain a natural description of th…
View article: On projectional skeletons in Vašák spaces
On projectional skeletons in Vašák spaces Open
We provide an alternative proof of the theorem saying that any Va\v{s}\'ak (or, weakly countably determined) Banach space admits a full $1$-projectional skeleton. The proof is done with the use of the method of elementary submodels and is …