On Free Locally Convex Spaces

被引：1

作者：

Banakh, Taras ^{[1
,2
]}

Gabriyelyan, Saak ^{[3
]}

机构：

[1] Ivan Franko Natl Univ Lviv, Lvov, Ukraine

[2] Jan Kochanowski Univ, Kielce, Poland

[3] Ben Gurion Univ Negev, Dept Math, Beer Sheva, Israel

来源：

FILOMAT | 2022年 / 36卷 / 18期

关键词：

(d f)-space; b-feral; c[!sub]0[!/sub]-quasibarrelled; free locally convex space; Grothendieck property;

D O I：

10.2298/FIL2218393B

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let L(X) be the free locally convex space over a Tychonoff space X. We prove that the following assertions are equivalent: (i) every functionally bounded subset of X is finite, (ii) L(X) is semi-reflexive, (iii) L(X) has the Grothendieck property, (iv) L(X) is semi-Montel. We characterize those spaces X, for which L(X) is c0-quasibarrelled, distinguished or a (d f)-space. If X is a convergent sequence, then L(X) has the Glicksberg property, but the space L(X) endowed with its Mackey topology does not have the Schur property.

引用

页码：6393 / 6401

页数：9

共 50 条

[41] Locally convex spaces with Toeplitz decompositions
Paúl, PJ
Sáez, C
Virués, JM
[J]. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 2000, 68 : 19 - 40
[42] PROBLEM OF MOMENTS IN LOCALLY CONVEX SPACES
RETAKH, VS
[J]. DOKLADY AKADEMII NAUK SSSR, 1973, 209 (03): : 562 - 564
[43] On the super efficiency in locally convex spaces
Wantao, Fu
Yonghong, Cheng
[J]. Nonlinear Analysis, Theory, Methods and Applications, 2001, 44 (06): : 821 - 828
[44] METRIZABLE LOCALLY CONVEX-SPACES
VALDIVIA, M
[J]. ARCHIV DER MATHEMATIK, 1976, 27 (01) : 79 - 85
[45] Drop property on locally convex spaces
Monterde, Ignacio
Montesinos, Vicente
[J]. STUDIA MATHEMATICA, 2008, 185 (02) : 143 - 149
[46] PERTURBATION OF SEMIGROUPS ON LOCALLY CONVEX SPACES
DEMBART, B
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 79 (05) : 986 - 991
[47] On some locally convex FK spaces
Leonetti, Paolo
Orhan, Cihan
[J]. TOPOLOGY AND ITS APPLICATIONS, 2022, 322
[48] HEREDITARY PROPERTY IN LOCALLY CONVEX SPACES
VALDIVIA, M
[J]. ANNALES DE L INSTITUT FOURIER, 1971, 21 (02) : 1 - &
[49] CONVERGENCE AND LOCALLY CONVEX-SPACES
MIKUSINSKI, J
[J]. BULLETIN DE L ACADEMIE POLONAISE DES SCIENCES-SERIE DES SCIENCES MATHEMATIQUES ASTRONOMIQUES ET PHYSIQUES, 1975, 23 (11): : 1171 - 1173
[50] Algebraic splines in locally convex spaces
Kolesnikov, AP
[J]. MATHEMATICAL NOTES, 2005, 77 (3-4) : 311 - 325

← 1 2 3 4 5 →