# Linear topological properties of the Lumer-Smirnov class of the polydisc

Studia Mathematica (1992)

- Volume: 102, Issue: 1, page 87-102
- ISSN: 0039-3223

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topNawrocki, Marek. "Linear topological properties of the Lumer-Smirnov class of the polydisc." Studia Mathematica 102.1 (1992): 87-102. <http://eudml.org/doc/215916>.

@article{Nawrocki1992,

abstract = {Linear topological properties of the Lumer-Smirnov class $LN_∗(^n)$ of the unit polydisc $^n$ are studied. The topological dual and the Fréchet envelope are described. It is proved that $LN_∗(^n)$ has a weak basis but it is nonseparable in its original topology. Moreover, it is shown that the Orlicz-Pettis theorem fails for $LN_∗(^n)$.},

author = {Nawrocki, Marek},

journal = {Studia Mathematica},

keywords = {linear topological properties of the Lumer-Smirnov class; topological dual; Fréchet envelope; weak basis; Orlicz-Pettis theorem},

language = {eng},

number = {1},

pages = {87-102},

title = {Linear topological properties of the Lumer-Smirnov class of the polydisc},

url = {http://eudml.org/doc/215916},

volume = {102},

year = {1992},

}

TY - JOUR

AU - Nawrocki, Marek

TI - Linear topological properties of the Lumer-Smirnov class of the polydisc

JO - Studia Mathematica

PY - 1992

VL - 102

IS - 1

SP - 87

EP - 102

AB - Linear topological properties of the Lumer-Smirnov class $LN_∗(^n)$ of the unit polydisc $^n$ are studied. The topological dual and the Fréchet envelope are described. It is proved that $LN_∗(^n)$ has a weak basis but it is nonseparable in its original topology. Moreover, it is shown that the Orlicz-Pettis theorem fails for $LN_∗(^n)$.

LA - eng

KW - linear topological properties of the Lumer-Smirnov class; topological dual; Fréchet envelope; weak basis; Orlicz-Pettis theorem

UR - http://eudml.org/doc/215916

ER -

## References

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