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Simpler Proof of the Ringrose’s Characterization of Compact Operators

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2015

Key Words:

Author Name
Abstract (2. Language): 
The aim of this note is to give short, simpler and elementary proof of one characterization of compact operators via orthonormal sequences, which, hopefully will make this fact more accessible to nonspecialists and to a wide audience (especially to students). Beside this, the proof given here shows that this fact holds true for operator acting from Hilbert space to some Banach (not necessarily Hilbert) space.
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  • English

REFERENCES

References: 

[1] J. H. Anderson and J. G. Stampfli. Commutators and compressions, Israel Journal of Mathematics,
10, 433-441. 1971.
[2] D. Bakic and B. Guljas. Which operators approximately annihilate orthonormal bases?, Acta
Scientiarum Mathematicarum (Szeged) 64, 601-607. 1998.
[3] P. A. Fillmore and J. P. Williams. On operator ranges, Advances in Mathematics 7, 254-281.
1971.
[4] K. Muroi and K.Tamaki. On Ringrose’s characterization of compact operators, Mathematica
Japonica 19, 259-261. 1974.
[5] J. R. Ringrose. Compact non-selfadjoint operators, Van Nostrand, Princeton, 1971.

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