6 papers · 1 filter
Continuous Linear Surjections from onto Symmetric Sequence Ideals in
Jerzy Kąkol, Wiesław Śliwa
Rosenthal's classical theorem says that, for every infinite compact space , the Banach space admits a quotient isomorphic to either or . The corresponding q…
On weak*-basic sequences in duals and biduals of spaces C(X) and Quojections
Jerzy Kakol, Manuel Lopez-Pellicer, Wieslaw Sliwa
We show that for infinite Tychonoff spaces X and Y the weak*-dual of Ck(X x Y) contains a basic sequence; moreover, the weak*-bidual of Ck(X) contains such a sequence as well. When…
An Elementary Proof Of The Josefson-Nissenzweig Theorem For Banach Spaces C(KxL)
Jerzy Kakol, Wiesław Śliwa
In [8] probabilistic methods, in particular a variant of the Weak Law of Large Numbers related to the Bernoulli distribution, have been used to show that for every infinite compact…
Lotz-Peck-Porta and Rosenthal's theorems for spaces
Jerzy Kąkol, Ondřej Kurka, Wiesław Śliwa
For a Tychonoff space by we denote the space of continuous real valued functions on endowed with the pointwise topology. We prove that an infinite compact s…
Josefson-Nissenzweig property for -spaces
T. Banakh, J. Kąkol, W. Śliwa
The famous Rosenthal-Lacey theorem asserts that for each infinite compact space the Banach space admits a quotient which is either a copy of or . The a…
On the separable quotient problem for Banach spaces
J. C. Ferrando, J. Kakol, M. Lopez-Pellicer +1
While the classic separable quotient problem remains open, we survey general results related to this problem and examine the existence of a particular infinitedimensional separable…