Buzano, Kreĭn and Cauchy-Schwarz inequalities
نویسندگان
چکیده
The Cauchy-Schwarz, Buzano and Kre\u{\i}n inequalities are three about inner product. main goal of this article is to present refinements Cauchy-Schwarz inequalities, a new proof refined version Kre\u{\i}n-type inequality. Applications that include Buzano-type for certain operators, operator norm numerical radius Hilbert space operators will be presented.
منابع مشابه
Strengthened Cauchy-schwarz and Hölder Inequalities
We present some identities related to the Cauchy-Schwarz inequality in complex inner product spaces. A new proof of the basic result on the subject of strengthened CauchySchwarz inequalities is derived using these identities. Also, an analogous version of this result is given for strengthened Hölder inequalities.
متن کاملInequalities related to the Cauchy-Schwarz inequality
We obtain an inequality complementary to the Cauchy-Schwarz inequality in Hilbert space. The inequalities involving first three powers of a self-adjoint operator are derived. The inequalities include the bounds for the third central moment, as a special case. It is shown that an upper bound for the spectral radius of a matrix is a root of a particular cubic equation, provided all eigenvalues ar...
متن کاملCauchy-schwarz Inequalities Associated with Positive Semideenite Matrices
Using a quasilinear representation for unitarily invariant norms, we prove a basic inequality: Let A = L X X M be positive semideenite, where X 2 M m;n. Then k jX j p k 2 kL p k kM p k for all p > 0 and all unitarily invariant norms k k. We show how several inequalities of Cauchy-Schwarz type follow from this bound and obtain a partial analog of our results for l p norms.
متن کاملReverse Cauchy–schwarz Inequalities for Positive C∗-valued Sesquilinear Forms
We prove two new reverse Cauchy–Schwarz inequalities of additive and multiplicative types in a space equipped with a positive sesquilinear form with values in a C *-algebra. We apply our results to get some norm and integral inequalities. As a consequence, we improve a celebrated reverse Cauchy–Schwarz inequality due to G. Pólya and G. Szegö.
متن کاملSome generalizations of the Cauchy-Schwarz and the Cauchy-Bunyakovsky inequalities involving four free parameters and their applications
Some generalizations of the well-known Cauchy-Schwarz inequality and the analogous Cauchy-Bunyakovsky inequality involving four free parameters are given for both discrete and continuous cases. Several particular cases of interest are also analyzed. Some of the applications of our main results include (for example) the Wagner inequality.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Operators and Matrices
سال: 2022
ISSN: ['1848-9974', '1846-3886']
DOI: https://doi.org/10.7153/oam-2022-16-19