- Tytuł:
- Topologies and bornologies determined by operator ideals, II
- Autorzy:
- Wong, Ngai-Ching
- Powiązania:
- https://bibliotekanauki.pl/articles/1290169.pdf
- Data publikacji:
- 1994
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
operator ideals
locally convex spaces
topologies
bornologies
Grothendieck spaces - Opis:
- Let be an operator ideal on LCS's. A continuous seminorm p of a LCS X is said to be - continuous if $Q̃_p ∈ ^{inj}(X,X̃_p)$, where $X̃_p$ is the completion of the normed space $X_p = X/p^{-1}(0)$ and $Q̃_p$ is the canonical map. p is said to be a Groth()- seminorm if there is a continuous seminorm q of X such that p ≤ q and the canonical map $Q̃_{pq} : X̃_q → X̃_p$ belongs to $(X̃_q,X̃_p)$. It is well known that when is the ideal of absolutely summing (resp. precompact, weakly compact) operators, a LCS X is a nuclear (resp. Schwartz, infra-Schwartz) space if and only if every continuous seminorm p of X is -continuous if and only if every continuous seminorm p of X is a Groth()-seminorm. In this paper, we extend this equivalence to arbitrary operator ideals and discuss several aspects of these constructions which were initiated by A. Grothendieck and D. Randtke, respectively. A bornological version of the theory is also obtained.
- Źródło:
-
Studia Mathematica; 1994, 111, 2; 153-162
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł