Let A be a positive (semidefinite) bounded linear operator on complex Hilbert space $$\big ({\mathcal {H}}, \langle \cdot , \rangle \big )$$ ( H ? · ? ) . The semi-inner product induced by is defined $${\langle x, y\rangle }_A := Ax, $$ x y : = for all $$x, y\in {\mathcal {H}}$$ ? and defines seminorm $${\Vert \Vert }_A$$ ? $${\mathcal This makes into semi-Hilbert space. For $$p\in [1,+\infty p...

Cauchy problem, 19, 136Condition number, 40, 55, 99, 110Contractibility, 183Counterflow equation, 156Critical delay, 167Delay Liapunov function, 138Delay margin, 170Departure from normality, 56Diagonalizable matrix, 55Diagonally dominant matrix, 36Differential inclusion, 45Dissipativity radius, 33Dual norm, 8, 25Dual pair, 25Eccentricity, ...

A modified Newton’s method which computes derivatives every other step is used to solve a nonlinear operator equation. An estimate of the radius of its convergence ball is obtained under Hölder continuous Fréchet derivatives in Banach space. An error analysis is given which matches its convergence order. 2010 Mathematics Subject Classification: 65B05, 47817, 49D15

In this paper distribution of zeros of solutions to functional equations in the spaces of discontinuous functions is studied. It will be demonstrated that oscillation properties of functional equations are determined by the spectral radius of a corresponding operator acting in the space of essentially bounded functions. Distances between zeros of solutions are estimated.

for a ∈ mn, the schur multiplier of a is defined as s a(x) =a ◦ x for all x ∈ mn and the spectral norm of s a can be stateas ∥s a∥ = supx,0 ∥a ∥x ◦x ∥ ∥. the other norm on s a can be definedas ∥s a∥ω = supx,0 ω(ω s( ax (x ) )) = supx,0 ωω (a (x ◦x ) ), where ω(a) standsfor the numerical radius of a. in this paper, we focus on therelation between the norm of schur multiplier of product of matric...

We consider the transitive linear maps on the operator algebra $B(X)$for a separable Banach space $X$. We show if a bounded linear map is norm transitive on $B(X)$,then it must be hypercyclic with strong operator topology. Also we provide a SOT-transitivelinear map without being hypercyclic in the strong operator topology.

‎let $x,y$ be normed spaces with $l(x,y)$ the space of continuous‎ ‎linear operators from $x$ into $y$‎. ‎if ${t_{j}}$ is a sequence in $l(x,y)$,‎ ‎the (bounded) multiplier space for the series $sum t_{j}$ is defined to be‎ [ ‎m^{infty}(sum t_{j})={{x_{j}}in l^{infty}(x):sum_{j=1}^{infty}%‎ ‎t_{j}x_{j}text{ }converges}‎ ‎]‎ ‎and the summing operator $s:m^{infty}(sum t_{j})rightarrow y$ associat...

in this paper, the operation of helix traveling wave tube in interaction region is investigated by using a three dimensional large signal lagrangian model in frequency domain. the complete simulation of these tubes is essential for optimum design and minimum manufacturing cost. this 3d code can compute interception current (or current losses ), beam radius changes in interaction region and the ...

In this paper, we consider the Bishop–Phelps–Bollobás point property for various classes of operators on complex Hilbert spaces, which is a stronger than property. We also deal with analogous problem by replacing norm an operator its numerical radius.