scholarly journals On characterization of non-Newtonian superposition operators in some sequence spaces

Filomat ◽  
2019 ◽  
Vol 33 (9) ◽  
pp. 2601-2612
Author(s):  
Birsen Sağır ◽  
Fatmanur Erdoğan
Keyword(s):  
Sequence Spaces ◽  
Real Sequence ◽  
Superposition Operator ◽  
Superposition Operators

In this paper, we define a non-Newtonian superposition operator NPf where f : N x R(N)? ? R(N)? by NPf (x) = (f(k,xk))? k=1 for every non-Newtonian real sequence x = (xk). Chew and Lee [4] have characterized Pf : ?p ? ?1 and Pf : c0 ? ?1 for 1 ? p < ?. The purpose of this paper is to generalize these works respect to the non-Newtonian calculus. We characterize NPf : ?? (N) ??1(N), NPf: c0(N)??1(N), NPf : c (N)? ?1 (N) and NPf : ?p (N) ? ?1 (N), respectively. Then we show that such NPf : ??(N) ? ?1 (N) is *-continuous if and only if f (k,.) is *-continuous for every k ? N.

scholarly journals Continuity of superposition operators on the double sequence spaces Lp

Filomat ◽  
2015 ◽  
Vol 29 (9) ◽  
pp. 2107-2118 ◽  
Author(s):  
Birsen Sağır ◽  
Nihan Güngör
Keyword(s):  
Double Sequence ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
Superposition Operator ◽  
Double Sequence Spaces ◽  
Superposition Operators ◽  
Necessary And Sufficient

In this paper, we define the superposition operator Pg where g : N2 x R ? R by Pg((xks))=g(k,s,xks) for all real double sequence (xks). Chew & Lee [4] and Petranuarat & Kemprasit [7] have characterized Pg : lp ? l1 and Pg : lp ? lq where 1 ? p,q < ?, respectively. The main goal of this paper is to construct the necessary and sufficient conditions for the continuity of Pg: Lp ? L1 and Pg : Lp ? Lq where 1 ? p,q < ?.

Entropy numbers of embedding maps between Besov spaces with an application to eigenvalue problems

1981 ◽  
Vol 90 (1-2) ◽  
pp. 63-70 ◽  
Author(s):  
Bernd Carl
Keyword(s):  
Banach Space ◽  
Asymptotic Behaviour ◽  
Besov Spaces ◽  
Eigenvalue Problems ◽  
Function Spaces ◽  
Sequence Spaces ◽  
Entropy Numbers ◽  
Diagonal Operators

SynopsisIn this paper we determine the asymptotic behaviour of entropy numbers of embedding maps between Besov sequence spaces and Besov function spaces. The results extend those of M. Š. Birman, M. Z. Solomjak and H. Triebel originally formulated in the language of ε-entropy. It turns out that the characterization of embedding maps between Besov spaces by entropy numbers can be reduced to the characterization of certain diagonal operators by their entropy numbers.Finally, the entropy numbers are applied to the study of eigenvalues of operators acting on a Banach space which admit a factorization through embedding maps between Besov spaces.The statements of this paper are obtained by results recently proved elsewhere by the author.

Some criteria for nuclearity

1986 ◽  
Vol 100 (1) ◽  
pp. 151-159 ◽  
Author(s):  
M. A. Sofi
Keyword(s):  
Sequence Space ◽  
Convex Space ◽  
Locally Convex Space ◽  
Sequence Spaces ◽  
Bilinear Forms ◽  
Simple Formulation ◽  
Normal Topology ◽  
Nuclear Spaces ◽  
Locally Convex

For a given locally convex space, it is always of interest to find conditions for its nuclearity. Well known results of this kind – by now already familiar – involve the use of tensor products, diametral dimension, bilinear forms, generalized sequence spaces and a host of other devices for the characterization of nuclear spaces (see [9]). However, it turns out, these nuclearity criteria are amenable to a particularly simple formulation in the setting of certain sequence spaces; an elegant example is provided by the so-called Grothendieck–Pietsch (GP, for short) criterion for nuclearity of a sequence space (in its normal topology) in terms of the summability of certain numerical sequences.

scholarly journals Biorthogonality in the real sequence spaces ℓp

1997 ◽  
Vol 40 (2) ◽  
pp. 325-330
Author(s):  
Anthony J. Felton ◽  
H. P. Rogosinski
Keyword(s):  
Linear Subspace ◽  
Sequence Spaces ◽  
Inner Product ◽  
Real Sequence ◽  
Closed Linear Subspace ◽  
The Real ◽  
Infinite Dimensional

In this paper we generalise some of the results obtained in [1] for the n-dimensional real spaces ℓp(n) to the infinite dimensional real spaces ℓp. Let p >1 with p ≠ 2, and let x be a non-zero real sequence in ℓp. Let ε(x) denote the closed linear subspace spanned by the set of all those sequences in ℓp which are biorthogonal to x with respect to the unique semi-inner-product on ℓp consistent with the norm on ℓp. In this paper we show that codim ε(x)=1 unless either x has exactly two non-zero coordinates which are equal in modulus, or x has exactly three non-zero coordinates α, β, γ with |α| ≥ |β| ≥ |γ| and |α|p > |β|p + |γ|p. In these exceptional cases codim ε(x) = 2. We show that is a linear subspace if, and only if, x has either at most two non-zero coordinates or x has exactly three non-zero coordinates which satisfy the inequalities stated above.

scholarly journals On the Characterization of Some Classes of Four-Dimensional Matrices and Almost B-Summable Double Sequences

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Orhan Tug
Keyword(s):  
Double Sequence ◽  
Sequence Spaces ◽  
Double Sequences ◽  
Matrix Classes ◽  
Related Literature ◽  
Double Sequence Spaces

We firstly summarize the related literature about Br,s,t,u-summability of double sequence spaces and almost Br,s,t,u-summable double sequence spaces. Then we characterize some new matrix classes of Ls′:Cf, BLs′:Cf, and Ls′:BCf of four-dimensional matrices in both cases of 0<s′≤1 and 1<s′<∞, and we complete this work with some significant results.

scholarly journals A characterization of a class of barrelled sequence spaces

1978 ◽  
Vol 19 (1) ◽  
pp. 27-31 ◽  
Author(s):  
J. Swetits
Keyword(s):  
Explicit Form ◽  
Sequence Spaces

In a recent paper [4] Bennett and Kalton characterized dense, barrelled subspaces of an arbitrary FK space, E. In this note, it is shown that if E is assumed to be an AK space, then the characterization assumes a simpler and more explicit form.

LOCAL BOUNDEDNESS OF NONAUTONOMOUS SUPERPOSITION OPERATORS IN

2015 ◽  
Vol 92 (2) ◽  
pp. 325-341 ◽  
Author(s):  
PIOTR KASPRZAK ◽  
PIOTR MAĆKOWIAK
Keyword(s):  
Bounded Variation ◽  
Bounded Function ◽  
Functions Of Bounded Variation ◽  
Superposition Operator ◽  
Local Boundedness ◽  
Superposition Operators ◽  
Locally Bounded Function

The main goal of this paper is to give the answer to one of the main problems of the theory of nonautonomous superposition operators acting in the space of functions of bounded variation in the sense of Jordan. Namely, we prove that if the superposition operator maps the space $BV[0,1]$ into itself, then it is automatically locally bounded, provided its generator is a locally bounded function.

Sign in / Sign up

Export Citation Format

Share Document