Geodesic
Generalized Buzano inequality
Filomat, Tome 37 (2023) no. 27, p. 9377

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DOI

If P is an orthogonal projection defined on an inner product space H, then the inequality |〈Px, y〉| ≤ 1 2 [∥x∥∥y∥ + |〈x, y〉|] fulfills for any x, y ∈ H (see [10]). In particular, when P is the identity operator, then it recovers the famous Buzano inequality. We obtain generalizations of such classical inequality, which hold for certain families of bounded linear operators defined on H. In addition, several new inequalities involving the norm and numerical radius of an operator are established.
DOI : 10.2298/FIL2327377B
Classification : 46C05, 26D15, 47B65, 47A12
Keywords: Buzano inequality, Cauchy-Schwarz inequality, Inner product space, Hilbert space, Bounded linear operator 
Tamara Bottazzi; Cristian Conde. Generalized Buzano inequality. Filomat, Tome 37 (2023) no. 27, p. 9377 . doi: 10.2298/FIL2327377B
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     author = {Tamara Bottazzi and Cristian Conde},
     title = {Generalized {Buzano} inequality},
     journal = {Filomat},
     pages = {9377 },
     year = {2023},
     volume = {37},
     number = {27},
     doi = {10.2298/FIL2327377B},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2327377B/}
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