# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## On positive embeddings of $C(K)$ spaces

### Tom 216 / 2013

Studia Mathematica 216 (2013), 179-192 MSC: Primary 46B26, 46B03, 46E15. DOI: 10.4064/sm216-2-5

#### Streszczenie

We investigate isomorphic embeddings $T: C(K)\to C(L)$ between Banach spaces of continuous functions. We show that if such an embedding $T$ is a positive operator then $K$ is the image of $L$ under an upper semicontinuous set-function having finite values. Moreover we show that $K$ has a $\pi$-base of sets whose closures are continuous images of compact subspaces of $L$. Our results imply in particular that if $C(K)$ can be positively embedded into $C(L)$ then some topological properties of $L$, such as countable tightness or Fréchetness, are inherited by $K$.

We show that some isomorphic embeddings $C(K)\to C(L)$ can be, in a sense, reduced to positive embeddings.

#### Autorzy

• Grzegorz PlebanekInstytut Matematyczny
Uniwersytet Wrocławski
Pl. Grunwaldzki 2/4
50-384 Wrocław, Poland
e-mail

## Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek