Compact Operators on Hilbert Spaces ()
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).
Share and Cite:
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.
|