# Linear operators on non-locally convex Orlicz spaces

Banach Center Publications (2008)

- Volume: 79, Issue: 1, page 157-165
- ISSN: 0137-6934

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topMarian Nowak, and Agnieszka Oelke. "Linear operators on non-locally convex Orlicz spaces." Banach Center Publications 79.1 (2008): 157-165. <http://eudml.org/doc/282076>.

@article{MarianNowak2008,

abstract = {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.},

author = {Marian Nowak, Agnieszka Oelke},

journal = {Banach Center Publications},

keywords = {Orlicz spaces; Lebesgue topology; modular topology; -smooth operators; Bochner integral representation; Radon-Nikodym property},

language = {eng},

number = {1},

pages = {157-165},

title = {Linear operators on non-locally convex Orlicz spaces},

url = {http://eudml.org/doc/282076},

volume = {79},

year = {2008},

}

TY - JOUR

AU - Marian Nowak

AU - Agnieszka Oelke

TI - Linear operators on non-locally convex Orlicz spaces

JO - Banach Center Publications

PY - 2008

VL - 79

IS - 1

SP - 157

EP - 165

AB - 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.

LA - eng

KW - Orlicz spaces; Lebesgue topology; modular topology; -smooth operators; Bochner integral representation; Radon-Nikodym property

UR - http://eudml.org/doc/282076

ER -

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