The symmetric shape of some inequalities between two sequences real numbers generates the same in operator theory. In this paper, we study a new refinement Cauchy–Bunyakovsky–Schwarz inequality for Euclidean spaces and several bounded linear operators on Hilbert space, where mention Bohr’s Bergström’s operators. We present an type operators, by technique monotony sequence. also prove Aczél spac...

We develop a representation of the second kind for certain Hardy classes solutions to nonhomogeneous Cauchy–Riemann equations and use it show that boundary values in sense distributions these functions can be represented as sum an atomic decomposition error term. continuity Hilbert transform on this class Schwarz-type value problem constructed associated classes.

In this work, a refinement of the Cauchy–Schwarz inequality in inner product space is proved. A more general Kato’s or so called mixed Schwarz established. Refinements some famous numerical radius inequalities are also pointed out. As shown these refinements generalize and refine recent old results obtained literature. Among others, it proved that if $$T\in \mathscr {B}\left( {H}\right) $$ , th...

We fully characterize orthogonal projections of infinite right circular (round) cones in real Hilbert spaces. Another interpretation is that, given two vectors in a real Hilbert space, we establish the optimal estimate on the angle between the orthogonal projections of the two vectors. The estimate depends on the angle between the two vectors and the position of only one of the two vectors. Our...

Recent developments in the theory and application of the HardyLittlewood method are discussed, concentrating on aspects associated with diagonal diophantine problems. Recent efficient differencing methods for estimating mean values of exponential sums are described first, concentrating on developments involving smooth Weyl sums. Next, arithmetic variants of classical inequalities of Bessel and ...

For functions belonging to each of the subclasses Mn (α) and N ∗ n (α) of normalized analytic functions in open unit disk U, which are introduced and investigated in this paper, the authors derive several properties involving their generalized convolution by applying certain techniques based especially upon the Cauchy-Schwarz and Hölder inequalities. A number of interesting consequences of thes...

Among all linear operators on Hilbert spaces, the compact ones (defined below) are the simplest, and most closely imitate finite-dimensional operator theory. In addition, compact operators are important in practice. We prove a spectral theorem for self-adjoint compact operators, which does not use broader discussions of properties of spectra, only using the Cauchy-Schwarz-Bunyakowsky inequality...