A Remark about the Scalar-Plus-Compact Problem
نویسندگان
چکیده
In [GM] a Banach space X was constructed such that every operator from a subspace Y ⊂ X into the space is of the form λIY→X +S, where IY→X is the inclusion map and S is strictly singular. In this paper we show that there is an operator T from a subspace Y ⊂ X into X which is not of the form λIY→X + K with K compact.
منابع مشابه
A remark on Remainders of homogeneous spaces in some compactifications
We prove that a remainder $Y$ of a non-locally compact rectifiable space $X$ is locally a $p$-space if and only if either $X$ is a Lindel"{o}f $p$-space or $X$ is $sigma$-compact, which improves two results by Arhangel'skii. We also show that if a non-locally compact rectifiable space $X$ that is locally paracompact has a remainder $Y$ which has locally a $G_{delta}$-diagonal, then...
متن کاملEvolution of the first eigenvalue of buckling problem on Riemannian manifold under Ricci flow
Among the eigenvalue problems of the Laplacian, the biharmonic operator eigenvalue problems are interesting projects because these problems root in physics and geometric analysis. The buckling problem is one of the most important problems in physics, and many studies have been done by the researchers about the solution and the estimate of its eigenvalue. In this paper, first, we obtain the evol...
متن کاملA General Scalar-Valued Gap Function for Nonsmooth Multiobjective Semi-Infinite Programming
For a nonsmooth multiobjective mathematical programming problem governed by infinitely many constraints, we define a new gap function that generalizes the definitions of this concept in other articles. Then, we characterize the efficient, weakly efficient, and properly efficient solutions of the problem utilizing this new gap function. Our results are based on $(Phi,rho)-$invexity,...
متن کاملEnsembles and experiments in classical and quantum physics
theorem amsfonts cmr5 [dvips]epsfig Enhancements to Picture Environment. Version 1.2 Released June 1, 1986 @multicnt @lta delta @delta gridcnt @jointhem ointhemfalse @firstpoint irstpointtrue joinkind dotgap ddotgap x@diff y@diff @diff @diff dotbox @segments @segmentsi @done @flippedargs @toosmall @drawit @horvline @stillmore datafile 0.4pt 1mm 1.2 20pt plus 3pt minus 3pt 20pt plus 3pt minus 3p...
متن کاملWarped product and quasi-Einstein metrics
Warped products provide a rich class of physically significant geometric objects. Warped product construction is an important method to produce a new metric with a base manifold and a fibre. We construct compact base manifolds with a positive scalar curvature which do not admit any non-trivial quasi-Einstein warped product, and non compact complete base manifolds which do not admit any non-triv...
متن کامل