For Banach spaces X and Y, a bounded linear operator T:X⟶Y⁎ is said to weak-star quasi attains its norm if the σ(Y⁎,Y)-closure of image by T unit ball intersects sphere radius ‖T‖ centered at origin in Y⁎. This notion inspired quasi-norm attainment operators introduced studied [5]. As main result, we prove that set attaining dense space regardless choice spaces, furthermore, approximating can b...

Given two Banach spaces X and Y, we introduce study a concept of norm-attainment in the space nuclear operators $$\mathcal N(X,Y)$$ projective tensor product $$X\widehat{\otimes }_\pi Y$$ . We exhibit positive negative examples where both previous hold. also problem whether class elements which attain their norms is dense or not. prove that, for concepts, density norm-attaining holds large Y wh...

In this note we offer a short, constructive proof for Hilbert spaces of Lindenstrauss’ famous result on the denseness of norm attaining operators. Specifically, we show given any A ∈ L(H) there is a sequence of rank-1 operators Kn such that A+Kn is norm attaining for each n and Kn converges in norm to zero. We then apply our construction to establish denseness results for norm attaining operato...