Schwarz inequality
Reverses of the Cauchy-Bunyakovsky-Schwarz Inequality for n-tuples of Complex Numbers
... The case where the disk ¯ D (α, r) does not contain the origin, i.e., |α| > r, provides the following interesting reverse of the Cauchy-Bunyakovsky-Schwarz inequality. Theorem 2. Let a, b, p as in ...
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More results on a functional generalization of the Cauchy Schwarz inequality
... above inequality gives the same result as the pre-Grüss inequality () while for p = q = (or p = q = ) the Cauchy-Schwarz inequality is ...Wagner inequality [] is derived. An ...
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A Generalization of the Cauchy-Schwarz Inequality with Four Free Parameters and Applications
... 3.1.2. Sub-case 2. p = s ∈ [−2, 0] (A refinement for the Cauchy-Schwarz inequality). Suppose in (3.1) that p = s ∈ [−2, 0] and p(p + 2) = u. Consequently u ∈ [−1, 0]. By noting these assumptions we can ...
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Reverses of the Schwarz Inequality in Inner Product Spaces and Applications
... Recent reverses for the celebrated Schwarz inequality in inner product spaces and applications for discrete and integral inequalities are sur- veyed1. Introduction.[r] ...
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Norm Inequalities for Sequences of Operators Related to the Schwarz Inequality
... Some norm inequalities for sequences of linear operators defined on Hilbert spaces that are related to the classical Schwarz inequality are given.. Applications for vector inequalities a[r] ...
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Some Inequalities for Power Series of Selfadjoint Operators in Hilbert Spaces via Reverses of the Schwarz Inequality
... Abstract. In this paper we obtain some operator inequalities for functions de…ned by power series with real coe¢ cients and, more speci…cally, with non- negative coe¢ cients. In order to obtain these inequalities some ...
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Reverses of the Schwarz Inequality in Inner Product Spaces Generalising a Klamkin-Mclenaghan Result
... As pointed out in [4], the above results are motivated by the fact that they generalise to the case of real or complex inner product spaces some classical reverses of the Cauchy-Bunyakovsky-Schwarz ...
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Generalizations of Cauchy Schwarz inequality in unitary spaces
... The Cauchy-Schwarz inequality is one of the most important inequalities in mathemat- ics. To date, a large number of generalizations and refinements of the inequalities (.) and (.) have been investigated ...
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Refinements of the Cauchy-Bunyakovsky-Schwarz Inequality for Functions of Selfadjoint Operators in Hilbert Spaces
... Theorem 4 . Let (ϕ, ψ) be a (DEC)-pair of continuous functions on [0, ∞) × [0, ∞) . If A, B are selfadjoint operators on the Hilbert space (H ; h., .i) with Sp (A) , Sp (B) ⊆ [m, M ] for some scalars m < M and if f ...
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A Generalization of the Cauchy Schwarz Inequality with Eight Free Parameters
... The results of the recent published paper by Masjed-Jamei et al. 2009 are extended to a larger class and some of subclasses are studied in the sequel. In other words, we generalize the well known Cauchy-Schwarz ...
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Some Results Related to the Cauchy-Bunyakovsky-Schwarz Inequality
... DRAGOMIR, Advances in Inequalities of the Schwarz, Gr¨ uss and Bessel Type in Inner Product Spaces, Nova Science Publishers, Inc., NY, 2005.. [5] Y.-C.[r] ...
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Further Inequalities for Sequences and Power Series of Operators in Hilbert Spaces Via Hermitian Forms
... Hermitian forms, Inner product, Hilbert space, Schwarz inequality, Numerical radius, Operator norm, Functions of operators.. This article is published with open access by Sidi Mohamed Be[r] ...
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Generalized Norms Inequalities for Absolute Value Operators
... In this section, we generalize some unitarily invariant norms inequalities for ab- solute value operators. Our results based on several lemmas. First two lemmas contain norm inequalities of Minkowski type and generalized ...
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Two Mappings Related To Semi-Inner Products And Their Applications in Geometry of Normed Linear Spaces
... the Schwarz inequality, applications to the Birkhoff orthogonality, to smoothness of normed linear spaces as well as to the characterization of best ...
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RRRR Specifically the dot product of two vectors a
... – Schwarz inequality allows one to define a notion of “the angle between the two vectors” for an arbitrary inner product, where the extendibility of such concepts from Euclidean geometry may not be ...
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A note on the Frobenius conditional number with positive definite matrices
... generalized Schwarz inequality, we present some lower bounds for the Frobenius condition number of a positive definite matrix depending on its trace, determinant, and Frobenius ...
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New Reverse Inequalities for Normal Operators in Hilbert Spaces
... Some of the obtained results are based on recent reverse results for the Schwarz inequality in Hilbert spaces due to the author1. Numerical radius, Bounded linear operators, Normal opera[r] ...
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Recent developments of Schwarz's type trace inequalities for operators in Hilbert spaces
... Abstract. In this paper, we survey some recent trace inequalities for oper- ators in Hilbert spaces that are connected to Schwarz’s, Buzano’s and Kato’s inequalities and the reverses of Schwarz inequality ...
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Spectral Radii of Operators and High-Power Operator Inequalities
... Theorem 1. Let T ≥ 0, and S and C be arbitrary operators. Also let T S, T C, A and B be all selfadjoint operators. If n is a positive integer, then for all x, y ∈ H, y 6= x, the following are equivalent to one another ...
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Mathematical Uncertainty Relations and their Generalization for Multiple Incompatible Observables
... Abstract: We show that the famous Heisenberg uncertainty relation for two incompatible observables can be generalized elegantly to the determinant form for N arbitrary observables. To achieve this purpose, we propose a ...
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