query: If every linear operator on a normed space bounded, is it possible to infer that the space is finite dimensional
positive_passages.docid: 28685
positive_passages.text: If every linear operator on $X$ is bounded then is $\dim X<\infty$?
negative_passages.docid: 154226
negative_passages.text: Upper bound for norm of Hilbert space operator
negative_passages.docid: 97949
negative_passages.text: Existence of a $\mathbb C$-Banach space isometric to a Hilbert Space but whose norm is not induced by an inner product?
negative_passages.docid: 95481
negative_passages.text: The set of self-adjoint operators over a Hilbert space doesn't form a lattice
negative_passages.docid: 93062
negative_passages.text: Is Every Invariant Subspace the Kernel of an polynomial applied in the operator?
negative_passages.docid: 108781
negative_passages.text: $A$ and $B$ are bounded linear operators from the normed linear space $X$ to itself. If $AB$ is invertible are $A$ and $B$ invertible?
negative_passages.docid: 92510
negative_passages.text: Proving a vector space is infinite-dimensional
negative_passages.docid: 52935
negative_passages.text: Do eigenvectors of quantum operators span the whole Hilbert Space?
negative_passages.docid: 112024
negative_passages.text: Let $T:V → V$ be a linear transformation where $V$ is finite dimensional.
negative_passages.docid: 63608
negative_passages.text: Cauchy sequence in a normed space
negative_passages.docid: 53850
negative_passages.text: Proof that every normed vector space is a topological vector space
negative_passages.docid: 18373
negative_passages.text: Can infinite-dimensional vector spaces be decomposed into direct sum of its subspaces?
negative_passages.docid: 83054
negative_passages.text: Let $E$ be a Banach space, prove that the sum of two closed subspaces is closed if one is finite dimensional
negative_passages.docid: 69206
negative_passages.text: A finite-dimensional vector space cannot be covered by finitely many proper subspaces?
negative_passages.docid: 112548
negative_passages.text: Existence of non-trivial linear functional on any vector space
negative_passages.docid: 124959
negative_passages.text: Does weak compactness imply boundedness in a normed vector space (not necessarily complete)?
negative_passages.docid: 109632
negative_passages.text: Show reflexive normed vector space is a Banach space