Locally m-pseudoconvex topologies on locally A-pseudoconvex algebras

M. Abel; J. Arhippainen

Czechoslovak Mathematical Journal (2004)

  • Volume: 54, Issue: 3, page 675-680
  • ISSN: 0011-4642

Abstract

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Let ( A , T ) be a locally A-pseudoconvex algebra over or . We define a new topology m ( T ) on A which is the weakest among all m-pseudoconvex topologies on A stronger than T . We describe a family of non-homogeneous seminorms on A which defines the topology m ( T ) .

How to cite

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Abel, M., and Arhippainen, J.. "Locally m-pseudoconvex topologies on locally A-pseudoconvex algebras." Czechoslovak Mathematical Journal 54.3 (2004): 675-680. <http://eudml.org/doc/30890>.

@article{Abel2004,
abstract = {Let $(A, T )$ be a locally A-pseudoconvex algebra over $\mathbb \{R\}$ or $\mathbb \{C\}$. We define a new topology $m (T)$ on $A$ which is the weakest among all m-pseudoconvex topologies on $A$ stronger than $T$. We describe a family of non-homogeneous seminorms on $A$ which defines the topology $m(T)$.},
author = {Abel, M., Arhippainen, J.},
journal = {Czechoslovak Mathematical Journal},
keywords = {locally A-pseudoconvex algebra; locally m-pseudoconvex algebra; locally -pseudoconvex algebra; locally -pseudoconvex algebra},
language = {eng},
number = {3},
pages = {675-680},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Locally m-pseudoconvex topologies on locally A-pseudoconvex algebras},
url = {http://eudml.org/doc/30890},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Abel, M.
AU - Arhippainen, J.
TI - Locally m-pseudoconvex topologies on locally A-pseudoconvex algebras
JO - Czechoslovak Mathematical Journal
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 3
SP - 675
EP - 680
AB - Let $(A, T )$ be a locally A-pseudoconvex algebra over $\mathbb {R}$ or $\mathbb {C}$. We define a new topology $m (T)$ on $A$ which is the weakest among all m-pseudoconvex topologies on $A$ stronger than $T$. We describe a family of non-homogeneous seminorms on $A$ which defines the topology $m(T)$.
LA - eng
KW - locally A-pseudoconvex algebra; locally m-pseudoconvex algebra; locally -pseudoconvex algebra; locally -pseudoconvex algebra
UR - http://eudml.org/doc/30890
ER -

References

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  8. The Open Mapping and Closed Graph Theorems in Topological Vector Spaces, Clarendon Press, Oxford, 1965. (1965) Zbl0124.06301MR0178331
  9. Topologies m-convexes dans les algebres A-convexes, Rend. Circ. Mat. Palermo XLI (1992), 397–406. (1992) Zbl0798.46043MR1230587
  10. Representation of locally convex algebras, Rev. Mat. Univ. Complut. Madrid 35 (1994), 233–244. (1994) Zbl0820.46047MR1297513
  11. Unité et semi-normes dans les algèbres localement convexes, Rev. Colombiana Mat. 16 (1982), 141–150. (1982) Zbl0565.46028MR0685249
  12. Banach Algebras and the General Theory of * -Algebras, Cambridge Univ. Press, New York, 1994. (1994) Zbl0809.46052
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