Compact Operators on Hilbert Spaces

DOI: 10.4236/oalib.1100853   PDF        2,331 Downloads   3,056 Views  

Abstract

In this paper, we obtain some results on compact operators. More specially, we prove that if T is a unitary operator on a Hilbert space H, then it is compact if and only if H has a finite dimension. Also, we prove that, if H is a Hilbert space with Heine-Borel property, then K(H) = BL(H).

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Nozari, S. (2014) Compact Operators on Hilbert Spaces. Open Access Library Journal, 1, 1-3. doi: 10.4236/oalib.1100853.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] Spurny, J. (2007) A Note on Compact Operators on Normed Linear Spaces. Expositiones Mathematicae, 25, 261-263.
http://dx.doi.org/10.1016/j.exmath.2006.11.002
[2] De la Sen, M. (2013) On a Class of Self-Adjoint Compact Operators in Hilbert Spaces and Their Relations with Their Finite-Range Truncations. Abstract and Applied Analysis, 2013, 1-15.
[3] Baker, J.M. (1979) A Note On Compact Operators Which Attain Their Norm. Pacific Journal of Mathematics, 82, 319-325.
http://dx.doi.org/10.2140/pjm.1979.82.319
[4] Thamban Nair, M. (2002) Functional Analysis-A First Course. Prentice-Hall, New Delhi.
[5] Rudin, W. (1973) Functional Analysis. McGraw-Hill, New York.

  
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