scholarly journals A sufficient condition for the Wold-Cramér concordance of Banach-space-valued stationary processes

1989 ◽  
Vol 14 ◽  
pp. 257-263
Author(s):  
Grazyna Hajduk-Chmielewska
Keyword(s):  
Banach Space ◽  
Stationary Processes ◽  
Sufficient Condition

scholarly journals A note on best approximation and invertibility of operators on uniformly convex Banach spaces

1991 ◽  
Vol 14 (3) ◽  
pp. 611-614 ◽  
Author(s):  
James R. Holub
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Banach Spaces ◽  
Best Approximation ◽  
Bounded Linear Operator ◽  
Convex Banach Space ◽  
Sufficient Condition ◽  
Uniformly Convex ◽  
Bounded Linear ◽  
Uniformly Convex Banach Spaces

It is shown that ifXis a uniformly convex Banach space andSa bounded linear operator onXfor which‖I−S‖=1, thenSis invertible if and only if‖I−12S‖<1. From this it follows that ifSis invertible onXthen either (i)dist(I,[S])<1, or (ii)0is the unique best approximation toIfrom[S], a natural (partial) converse to the well-known sufficient condition for invertibility thatdist(I,[S])<1.

scholarly journals On Weighted Polynomial Approximation With Gaps

2005 ◽  
Vol 178 ◽  
pp. 55-61 ◽  
Author(s):  
Guantie Deng
Keyword(s):  
Banach Space ◽  
Continuous Function ◽  
Polynomial Approximation ◽  
Continuous Functions ◽  
Sufficient Condition ◽  
Weighted Polynomial Approximation ◽  
Necessary And Sufficient Condition ◽  
Weighted Banach Space ◽  
Nonnegative Continuous Function ◽  
Necessary And Sufficient

Let α be a nonnegative continuous function on ℝ. In this paper, the author obtains a necessary and sufficient condition for polynomials with gaps to be dense in Cα, where Cα is the weighted Banach space of complex continuous functions ƒ on ℝ with ƒ(t) exp(−α(t)) vanishing at infinity.

scholarly journals On the modulus ofu-convexity of Ji Gao

2003 ◽  
Vol 2003 (1) ◽  
pp. 49-54 ◽  
Author(s):  
Eva María Mazcuñán-Navarro
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Normal Structure ◽  
Fixed Point Property ◽  
Sufficient Condition ◽  
Point Property

We consider the modulus ofu-convexity of a Banach space introduced by Ji Gao (1996) and we improve a sufficient condition for the fixed-point property (FPP) given by this author. We also give a sufficient condition for normal structure in terms of the modulus ofu-convexity.

ON BI-BANACH FRAMES IN BANACH SPACES

2014 ◽  
Vol 12 (02) ◽  
pp. 1450015 ◽  
Author(s):  
SHALU SHARMA
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Banach Frames ◽  
Banach Frame ◽  
Necessary And Sufficient

Bi-Banach frames in Banach spaces have been defined and studied. A necessary and sufficient condition under which a Banach space has a Bi-Banach frame has been given. Finally, Pseudo exact retro Banach frames have been defined and studied.

ON FRAME SYSTEMS IN BANACH SPACES

2009 ◽  
Vol 07 (01) ◽  
pp. 1-7 ◽  
Author(s):  
P. K. JAIN ◽  
S. K. KAUSHIK ◽  
NISHA GUPTA
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Bessel Sequence ◽  
Banach Frame ◽  
Frame System ◽  
Frame Systems ◽  
Necessary And Sufficient

Banach frame systems in Banach spaces have been defined and studied. A sufficient condition under which a Banach space, having a Banach frame, has a Banach frame system has been given. Also, it has been proved that a Banach space E is separable if and only if E* has a Banach frame ({φn},T) with each φn weak*-continuous. Finally, a necessary and sufficient condition for a Banach Bessel sequence to be a Banach frame has been given.

scholarly journals A further necessary and sufficient condition for strong convergence of nonlinear contraction semigroups and of iterative methods for accretive operators in Banach spaces

1995 ◽  
Vol 38 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Zong-Ben Xu ◽  
Yao-Lin Jiang ◽  
G. F. Roach
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Iterative Methods ◽  
Accretive Operator ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Accretive Operators ◽  
Uniformly Smooth ◽  
Necessary And Sufficient

Let A be a quasi-accretive operator defined in a uniformly smooth Banach space. We present a necessary and sufficient condition for the strong convergence of the semigroups generated by – A and of the steepest descent methods to a zero of A.

ON THE DECOMPOSITION OF OPERATORS WITH SEVERAL ALMOST-INVARIANT SUBSPACES

2019 ◽  
Vol 99 (2) ◽  
pp. 274-283
Author(s):  
AMANOLLAH ASSADI ◽  
MOHAMAD ALI FARZANEH ◽  
HAJI MOHAMMAD MOHAMMADINEJAD
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Closed Subspace ◽  
Invariant Subspaces ◽  
Weak Limit ◽  
Linear Operators ◽  
Sufficient Condition ◽  
Bounded Operators ◽  
Bounded Linear ◽  
Rank Operator

We seek a sufficient condition which preserves almost-invariant subspaces under the weak limit of bounded operators. We study the bounded linear operators which have a collection of almost-invariant subspaces and prove that a bounded linear operator on a Banach space, admitting each closed subspace as an almost-invariant subspace, can be decomposed into the sum of a multiple of the identity and a finite-rank operator.

THE VARIANCE OF AN INTEGRATED PROCESS NEED NOT DIVERGE TO INFINITY, AND RELATED RESULTS ON PARTIAL SUMS OF STATIONARY PROCESSES

2001 ◽  
Vol 17 (4) ◽  
pp. 671-685 ◽  
Author(s):  
Hannes Leeb ◽  
Benedikt M. Pötscher
Keyword(s):  
Sufficient Conditions ◽  
Partial Sums ◽  
Stationary Processes ◽  
Sufficient Condition ◽  
Integrated Process ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

For a process with stationary first differences a necessary and sufficient condition for the variance of the process to be unbounded is given. An example shows that the variance of an integrated process—although unbounded—need not diverge to infinity. Sufficient conditions for the variance of an integrated process to diverge to infinity are provided.

scholarly journals The approximation problem for compact operators

1969 ◽  
Vol 1 (3) ◽  
pp. 397-401 ◽  
Author(s):  
S.R. Caradus
Keyword(s):  
Banach Space ◽  
Unit Ball ◽  
Finite Rank ◽  
Reflexive Banach Space ◽  
Approximation Problem ◽  
Compact Operators ◽  
Sufficient Condition

The following sufficient condition is obtained for the uniform approximability of compact operators on a reflexive Banach space by operators of finite rank: if S is the unit ball of X and ø: X* → C(S) is the imbedding ø(x*)x = x*(x) then we require ø(X*) to be complemented in C(S).

FRAMES OF SUBSPACES FOR BANACH SPACES

2010 ◽  
Vol 08 (02) ◽  
pp. 243-252 ◽  
Author(s):  
P. K. JAIN ◽  
S. K. KAUSHIK ◽  
VARINDER KUMAR
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Banach Frame ◽  
Necessary And Sufficient ◽  
Compactly Generated

Frames of subspaces for Banach spaces have been introduced and studied. Examples and counter-examples to distinguish various types of frames of subspaces have been given. It has been proved that if a Banach space has a Banach frame, then it also has a frame of subspaces. Also, a necessary and sufficient condition for a sequence of projections, associated with a frame of subspaces, to be unique has been given. Finally, we consider complete frame of subspaces and prove that every weakly compactly generated Banach space has a complete frame of subspaces.

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