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On Pólya–Szegö reverse of Schwarz's inequality
Author(s) -
Otachel Zdzisław
Publication year - 2020
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201800485
Subject(s) - mathematics , cauchy–schwarz inequality , inequality , pure mathematics , product (mathematics) , hadamard product , kantorovich inequality , hölder's inequality , log sum inequality , rearrangement inequality , inner product space , hadamard transform , mathematical analysis , linear inequality , geometry
We present some new results on the Cauchy–Schwarz inequality in inner product spaces, where four vectors are involved. This naturally extends Pólya–Szegö reverse of Schwarz's inequality onto complex inner product spaces. Applications to the famous Hadamard's inequality about determinants and the triangle inequality for norms are given.