Operators that attain their minima

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• 作者：Xavier Carvajal (1)
  Wladimir Neves (1)
  
• 关键词：Hilbert spaces ; bounded operators ; spectral representation ; Primary ; 47B65 ; Secondary ; 47A58 ; 47A65 ; 47A12
• 刊名：Bulletin of the Brazilian Mathematical Society
• 出版年：2014
• 出版时间：June 2014
• 年：2014
• 卷：45
• 期：2
• 页码：293-312
• 全文大小：
• 参考文献：1. X. Carvajal and W. Neves. / Operators that achieve the norm. Integral Equations and Operator Theory, 72 (2012), 179鈥?95. CrossRef
  2. B. Chevreau. Personal communications.
  3. I. Chalendar. Techniques d鈥檃lg猫bres duales et sous-espaces invariants. (French) [Dual algebra techniques and invariant subspaces] With a preface in Romanian by Bernard Chevreau. Monografii Matematice (Timisoara) [Mathematical Monographs (Timisoara)], 55. Universitatea de Vest din Timisoara, Facultatea de Matematica, Timisoara, (1995), iv+94 pp.
  4. M. Fabian, P. Habala, P. H谩jek, V.M. Santaluc铆a, J. Pelant and V. Zizler. Functional Analysis and Infinite-Dimensional Geometry, CMS Books in Mathematics, Springer, New York (2001). CrossRef
  5. P.R. Halmos. Introduction to Hilbert space and the theory of spectral multiplicity, Chelsea, New York (1951).
  6. W. Rudin. Functional Analysis, McGraw-Hill, Inc., second edition (1991).
  
• 作者单位：Xavier Carvajal (1)
  Wladimir Neves (1)
  
  1. Instituto de Matem谩tica Universidade Federal do Rio de Janeiro, Cidade Universit谩ria, C.P. 68530, 21945-970, Rio de Janeiro, Brazil
  
• ISSN：1678-7714

文摘

In this paper we study the theory of operators on complex Hilbert spaces, which attain theirminima in the unit sphere. We prove someimportant results concerning the characterization of the N*, and also AN* operators, see respectively Definition 1.1 and Definition 1.4. The injective property plays an important role in these operators, and shall be established by these classes.