Barrelled locally convex spaces
著者
書誌事項
Barrelled locally convex spaces
(North-Holland mathematics studies, 131)(Notas de matemática, 113)
North-Holland, 1987
大学図書館所蔵 全40件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Bibliography: p. 483-506
Includes index
内容説明・目次
内容説明
This book is a systematic treatment of barrelled spaces, and of structures in which barrelledness conditions are significant. It is a fairly self-contained study of the structural theory of those spaces, concentrating on the basic phenomena in the theory, and presenting a variety of functional-analytic techniques.Beginning with some basic and important results in different branches of Analysis, the volume deals with Baire spaces, presents a variety of techniques, and gives the necessary definitions, exploring conditions on discs to ensure that they are absorbed by the barrels of the space. The abstract theory of barrelled spaces is then presented, as well as local completeness and its applications to the inheritance of the Mackey topology to subspaces. Further discussed is the abstract study of bornological and ultrabornological spaces; B- and Br-completeness; inductive limits; strong barrelledness conditions; characterizations of barrelled, bornological and (DF)-spaces in the context of spaces of type C(X); the stability of barrelledness conditions of topological tensor products and the related questions of commutability of inductive limits and tensor products; and the holomorphically significant properties of locally convex spaces as developed by Nachbin and others.
目次
1. Baire Linear Spaces. 2. Basic Tools. 3. Barrels and Discs. 4. Barrelled Spaces. 5. Local Completeness. 6. Bornological and Ultrabornological Spaces. 7. B- and Br-Completeness. 8. Inductive Limit Topologies. 9. Strong Barrelledness Conditions. 10. Locally Convex Properties of the Space of Continuous Functions Endowed with the Compact-Open Topology. 11. Barrelledness Conditions on Topological Tensor Products. 12. Holomorphically Significant Properties of Locally Convex Spaces. 13. A Short Collection of Open Problems. A Table of Barrelled Spaces. References. Index.
「Nielsen BookData」 より