About the Cauchy–Bunyakovsky–Schwarz Inequality for Hilbert Space Operators
The symmetric shape of some inequalities between two sequences of real numbers generates inequalities of the same shape in operator theory. In this paper, we study a new refinement of the Cauchy–Bunyakovsky–Schwarz inequality for Euclidean spaces and several inequalities for two bounded linear opera...
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MDPI AG
2021-02-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/2/305 |
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doaj-eba5c431bf454327b4c5131d2da5ea422021-02-12T00:00:20ZengMDPI AGSymmetry2073-89942021-02-011330530510.3390/sym13020305About the Cauchy–Bunyakovsky–Schwarz Inequality for Hilbert Space OperatorsNicuşor Minculete0Department of Mathematics and Computer Science, Transilvania University of Braşov, Iuliu Maniu Street, No. 50, 500091 Braşov, RomaniaThe symmetric shape of some inequalities between two sequences of real numbers generates inequalities of the same shape in operator theory. In this paper, we study a new refinement of the Cauchy–Bunyakovsky–Schwarz inequality for Euclidean spaces and several inequalities for two bounded linear operators on a Hilbert space, where we mention Bohr’s inequality and Bergström’s inequality for operators. We present an inequality of the Cauchy–Bunyakovsky–Schwarz type for bounded linear operators, by the technique of the monotony of a sequence. We also prove a refinement of the Aczél inequality for bounded linear operators on a Hilbert space. Finally, we present several applications of some identities for Hermitian operators.https://www.mdpi.com/2073-8994/13/2/305Cauchy–Bunyakovsky–Schwarz inequalityBohr’s inequalityBergström’s inequalityAczél inequality |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Nicuşor Minculete |
| spellingShingle |
Nicuşor Minculete About the Cauchy–Bunyakovsky–Schwarz Inequality for Hilbert Space Operators Symmetry Cauchy–Bunyakovsky–Schwarz inequality Bohr’s inequality Bergström’s inequality Aczél inequality |
| author_facet |
Nicuşor Minculete |
| author_sort |
Nicuşor Minculete |
| title |
About the Cauchy–Bunyakovsky–Schwarz Inequality for Hilbert Space Operators |
| title_short |
About the Cauchy–Bunyakovsky–Schwarz Inequality for Hilbert Space Operators |
| title_full |
About the Cauchy–Bunyakovsky–Schwarz Inequality for Hilbert Space Operators |
| title_fullStr |
About the Cauchy–Bunyakovsky–Schwarz Inequality for Hilbert Space Operators |
| title_full_unstemmed |
About the Cauchy–Bunyakovsky–Schwarz Inequality for Hilbert Space Operators |
| title_sort |
about the cauchy–bunyakovsky–schwarz inequality for hilbert space operators |
| publisher |
MDPI AG |
| series |
Symmetry |
| issn |
2073-8994 |
| publishDate |
2021-02-01 |
| description |
The symmetric shape of some inequalities between two sequences of real numbers generates inequalities of the same shape in operator theory. In this paper, we study a new refinement of the Cauchy–Bunyakovsky–Schwarz inequality for Euclidean spaces and several inequalities for two bounded linear operators on a Hilbert space, where we mention Bohr’s inequality and Bergström’s inequality for operators. We present an inequality of the Cauchy–Bunyakovsky–Schwarz type for bounded linear operators, by the technique of the monotony of a sequence. We also prove a refinement of the Aczél inequality for bounded linear operators on a Hilbert space. Finally, we present several applications of some identities for Hermitian operators. |
| topic |
Cauchy–Bunyakovsky–Schwarz inequality Bohr’s inequality Bergström’s inequality Aczél inequality |
| url |
https://www.mdpi.com/2073-8994/13/2/305 |
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