Application to Matrix Transformations
نویسنده
چکیده
Given any sequence τ = (τn)n≥1 of positive real numbers and any set E of complex sequences, we write Eτ for the set of all sequences x = (xn)n≥1 such that x/a = (xn/an)n≥1 ∈ E. We define the sets Wτ = (w∞)τ and W 0 τ = (w0)τ , where w∞ is the set of all sequences such that supn (n −1∑n m=1 |xm|) < ∞, and w0 is the set of all sequences such that limn→∞ (n−1 ∑n m=1 |xm|) = 0. Then we explicitly calculate the spectra σ (∆,Wτ ) and σ (∆,W 0 τ ) of the operator of the first difference on each of the sets Wτ and W 0 τ . We then determine the sets (E,F ) of all matrix transformations mapping E to F , with E = Wτ ( (∆− λI) ) , or W 0 τ ( (∆− λI) ) and F = sξ, or s 0 ξ for complex numbers λ and h and obtain simplifications of these sets for some values of λ.
منابع مشابه
An application of Fibonacci numbers into infinite Toeplitz matrices
The main purpose of this paper is to define a new regular matrix by using Fibonacci numbers and to investigate its matrix domain in the classical sequence spaces $ell _{p},ell _{infty },c$ and $c_{0}$, where $1leq p
متن کاملOn p-semilinear transformations
In this paper, we introduce $p$-semilinear transformations for linear algebras over a field ${bf F}$ of positive characteristic $p$, discuss initially the elementary properties of $p$-semilinear transformations, make use of it to give some characterizations of linear algebras over a field ${bf F}$ of positive characteristic $p$. Moreover, we find a one-to-one correspondence between $p$-semiline...
متن کاملApplication of measures of noncompactness to infinite system of linear equations in sequence spaces
G. Darbo [Rend. Sem. Math. Univ. Padova, 24 (1955) 84--92] used the measure of noncompactness to investigate operators whose properties can be characterized as being intermediate between those of contraction and compact operators. In this paper, we apply the Darbo's fixed point theorem for solving infinite system of linear equations in some sequence spaces.
متن کاملTransformations computations: Power, Roots and Inverse
This paper presents some results of an annihilated element in Banach algebra, and in specific case, for any square matrix. The developed method significantly improves the computational aspects of transformations calculus and especially for finding powers and roots of any annihilated element. An example is given to compare the proposed method with some other methods to show the efficienc...
متن کاملCoupled Bending-Longitudinal Vibration of Three Layer Sandwich Beam using Exact Dynamic Stiffness Matrix
A Newtonian (vectorial) approach is used to develop the governing differential equations of motion for a three layer sandwich beam in which the uniform distribution of mass and stiffness is dealt with exactly. The model allows for each layer of material to be of unequal thickness and the effects of coupled bending and longitudinal motion are accounted for. This results in an eighth order ordina...
متن کامل