A projection satisfying $\| Px \| \leq \|x\|$ for all $x$ is an orthogonal projection
18205
Orthogonal Projection
97158
Prove that the operator norm is a norm
46760
To show that $P(|X-Y| \leq 2) \leq 3P(|X-Y| \leq 1)$
143869
Showing that the norm of the canonical projection $X\to X/M$ is $1$
113779
If $P$ is an orthogonal matrix its columns form an orthonormal set.
17336
Least norm in convex set in Banach space
154913
Are all the norms of $L^p$ space equivalent?
149664
Norm is sup of inner products (proof).
43897
An integral inequality (Rudin $L^p$-spaces 3.12)
69474
Orthogonal projections with $\sum P_i =I$, proving that $i\ne j \Rightarrow  P_{j}P_{i}=0$
153634
A statment about the equivalence between the Axiom of Choice and the surjectivity of the projections.
146099
Why is this true: The only orthogonal projection that is also unitary from $\Bbb C^n$ to $\Bbb C^n$ is the identity
77217
Proof that a coordinate-wise convex function is convex?
103045
Composition of Proximal Operators
126165
Prove $|\arctan x - \arctan y|\leq |x-y|$
30017
Orthogonality and linear independence
86110
Proximal Operator Fixed Point Property for Matrices