Showing that linear operator is bounded
61931
Positive operator is bounded
124061
Prove the reciprocal of a function is integrable if it is bounded
56102
Prove that there is no non-zero linear operator on $\mathbb C^{2}$ such that $(\alpha | T\alpha) = 0$
129549
Showing that the orthogonal projection in a Hilbert space is compact iff the subspace is finite dimensional
112231
Showing that a one-to-one linear transformation maps a linearly independent set onto a linearly independent set
93121
How to prove there exists a linear transformation?
101776
Bounded solution for an equation
157455
Show that the norm of the multiplication operator $M_f$ on $L^2[0,1]$ is $\|f\|_\infty$
155317
Norm of adjoint operator in Hilbert space
144112
Show that $c_0$ is a Banach space with the norm $\rVert \cdot \lVert_\infty$
80279
Show that $S + T$ and $aT$ are linear
8805
Bounded linear operators that commute with translation
28678
Show that $A_n=\sum\limits_{k=1}^n \sin k $ is bounded?
18040
Show that a compact metric space is bounded
38896
Prove that $A$ is bounded operator on $\ell^p$ and find $\| A\|$
91911
A linear operator between $C[0,1]$ and $C[0,1]$ defined as $Tf = f + \int f$; Show $T$ is an isomorphism
32789
Show bounded harmonic function on $\mathbb{C}$ is constant.