Every Infinite-dimensional normed vector space containes a non continous linear functional
15820
Discontinuous linear functional
97949
Existence of a $\mathbb C$-Banach space isometric to a Hilbert Space but whose norm is not induced by an inner product?
140813
How do i prove that continuous linear transformation between normed spaces is bounded?
67283
Is $L^{p}$ space with alternate norm Banach?
107389
Show that the vector space of real functions is not finitely spanned
60655
$\ker T\subset \ker S\Rightarrow S=rT$ when $S$ and $T$ are linear functionals
120344
Are there nontrivial vector spaces with finitely many elements?
109632
Show reflexive normed vector space is a Banach space
19294
‎If ‎‎$‎X$ is an infinite-dimensional Banach space and ‎‎$‎‎u‎\in ‎B(X)‎$ ,then $\bigcap_{v\in K(X)}\sigma(u+v) =\cdots$
84448
Any positive linear functional $\phi$ on $\ell^\infty$ is a bounded linear operator and has $\|\phi \| = \phi((1,1,...)) $
90350
How can we replace $\sup$ with $\max$ in definition of subordinate norm for finite-dimensional vector space?
151467
An infinite generating set of a finite dimensional vector space contains a basis
83461
Continuous iff composition with every linear functional is continuous
17495
Show that the vector space of all continuous real-valued functions is infinite-dimensional
71001
Do continuous linear functions between Banach spaces extend?
146143
Question about proof that finite-dimensional subspaces of normed vector spaces are direct summands
119947
Can a non-zero vector have zero image under every linear functional?