Linear operators on non-locally convex Orlicz spaces

• Autorzy: Marian Nowak , Agnieszka Oelke
• Języki publikacji: EN

Abstrakty

EN

We study linear operators from a non-locally convex Orlicz space $L^Φ$ to a Banach space $(X,||·||_X)$. Recall that a linear operator $T:L^Φ → X$ is said to be σ-smooth whenever $uₙ\longrightarrow\limits^{(o)} 0$ in $L^Φ$ implies $||T(uₙ)||_X → 0$. It is shown that every σ-smooth operator $T:L^Φ → X$ factors through the inclusion map $j:L^Φ → L^{Φ̅}$, where Φ̅ denotes the convex minorant of Φ. We obtain the Bochner integral representation of σ-smooth operators $T:L^Φ → X$. This extends some earlier results of J. J. Uhl concerning the Bochner integral representation of linear operators defined on a locally convex Orlicz space.

Kategorie tematyczne

• 47B38: Operators on function spaces (general)
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2008
• Tom: 79
• Numer: 1
• Strony: 157-165

Daty

wydano

2008

Twórcy

autor

Marian Nowak

• Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Szafrana 4a, 65-516 Zielona Góra, Poland

autor

Agnieszka Oelke

• Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Szafrana 4a, 65-516 Zielona Góra, Poland

Identyfikatory

DOI

10.4064/bc79-0-12