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Adjoints and the image of the ball

Author: Fred Richman
Journal: Proc. Amer. Math. Soc. 129 (2001), 1189-1193
MSC (2000): Primary 03F65, 47A05
Published electronically: September 20, 2000
MathSciNet review: 1701689
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Abstract | References | Similar Articles | Additional Information


A bounded operator between Hilbert spaces has an adjoint if and only if the image of the unit ball is located.

References [Enhancements On Off] (What's this?)

  • 1. Errett Bishop and Douglas Bridges, Constructive analysis, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 279, Springer-Verlag, Berlin, 1985. MR 804042
  • 2. DOUGLAS BRIDGES, FRED RICHMAN AND PETER SCHUSTER, Adjoints, absolute values and polar decompositions, preprint (; J. Operator Theory (to appear).
  • 3. Douglas Bridges, Fred Richman, and Wang Yuchuan, Sets, complements and boundaries, Indag. Math. (N.S.) 7 (1996), no. 4, 425–445. MR 1620100, 10.1016/S0019-3577(97)89131-8
  • 4. Hajime Ishihara, Constructive compact operators on a Hilbert space, Ann. Pure Appl. Logic 52 (1991), no. 1-2, 31–37. International Symposium on Mathematical Logic and its Applications (Nagoya, 1988). MR 1104052, 10.1016/0168-0072(91)90037-M
  • 5. FRED RICHMAN, Generalized real numbers in constructive mathematics, Indag. Math. 9 (1998), 595-606. CMP 99:14

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Additional Information

Fred Richman
Affiliation: Department of Mathematics, Florida Atlantic University, Boca Raton, Florida 33431

Received by editor(s): January 8, 1999
Received by editor(s) in revised form: June 8, 1999
Published electronically: September 20, 2000
Communicated by: Carl G. Jockusch, Jr.
Article copyright: © Copyright 2000 American Mathematical Society