query: A question about bounded operators on banach space
positive_passages.docid: 151046
positive_passages.text: Closure of the invertible operators on a Banach space
negative_passages.docid: 149997
negative_passages.text: Convolution operator has norm 1 with respect to $L^2$ norm
negative_passages.docid: 28685
negative_passages.text: If every linear operator on $X$ is bounded then is $\dim X<\infty$?
negative_passages.docid: 92497
negative_passages.text: Isometric Embedding of a separable Banach Space into $\ell^{\infty}$
negative_passages.docid: 17262
negative_passages.text: Bounded operator that does not attain its norm
negative_passages.docid: 46326
negative_passages.text: The space $C[a,b]$ with $\|f\|:=\int_a^b |f(x)|d(x)$ is a normed space but not a Banach space
negative_passages.docid: 144656
negative_passages.text: Linear functional and a bounded norm
negative_passages.docid: 62428
negative_passages.text: How to prove this inequality in Banach space?
negative_passages.docid: 139367
negative_passages.text: Hahn Banach Theorem: Transfinite Induction
negative_passages.docid: 29836
negative_passages.text: Prove: Convergent sequences are bounded
negative_passages.docid: 133777
negative_passages.text: Application of Banach-Steinhaus theorem
negative_passages.docid: 121079
negative_passages.text: lemma: Cauchy sequences are bounded.
negative_passages.docid: 157455
negative_passages.text: Show that the norm of the multiplication operator $M_f$ on $L^2[0,1]$ is $\|f\|_\infty$
negative_passages.docid: 104914
negative_passages.text: Abount linear functional: If $T(B)$ is bounded, is $T$ bounded?
negative_passages.docid: 43146
negative_passages.text: Does an integral operator with a symmetric integrable kernel have to be bounded on $L^2$?
negative_passages.docid: 2439
negative_passages.text: If a linear operator has an adjoint operator, it is bounded
negative_passages.docid: 120648
negative_passages.text: Proof Check: Every Cauchy Sequence is Bounded