Abstract
If \(\{ E_{\lambda} \} _{\lambda\in\mathbb{R}}\) is the spectral family of a bounded selfadjoint operator A on a Hilbert space H and m=minSp(A) and M=maxSp(A), we show that for any continuous function φ: \([ m,M ] \rightarrow \mathbb{C}\), we have the inequality
for any vectors x and y from H. Some related results and applications are also given.
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The author would like to thank the anonymous referee for reading carefully the paper and providing some useful suggestions to improve it.
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Dragomir, S.S. Some inequalities for continuous functions of selfadjoint operators in hilbert spaces. Acta Math Vietnam 39, 287–303 (2014). https://doi.org/10.1007/s40306-014-0061-4
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DOI: https://doi.org/10.1007/s40306-014-0061-4
Keywords
- Selfadjoint operators
- Functions of selfadjoint operators
- Spectral representation
- Inequalities for selfadjoint operators