This is an announcement for the paper "Schauder bases and operator theory" by Yang Cao, Geng Tian, and Bingzhe Hou.

Abstract: In this paper, we firstly give a matrix approach to the bases of a separable Hilbert space and then correct a mistake appearing in both review and the English translation of the Olevskii's paper. After this, we show that even a diagonal compact operator may map an orthonormal basis into a conditional basis.

Archive classification: math.FA

Mathematics Subject Classification: Primary 47B37, 47B99, Secondary 54H20, 37B99

Remarks: 17 pages

Submitted from: caoyang@jlu.edu.cn

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1203.3603

or

http://arXiv.org/abs/1203.3603