query: Rudin Functional Analysis Chapter 2 Problem 16
positive_passages.docid: 27661
positive_passages.text: The closed graph theorem in topology
negative_passages.docid: 101619
negative_passages.text: Question involving the Cauchy-Goursat Theorem
negative_passages.docid: 16692
negative_passages.text: a representation condition of Hilbert space
negative_passages.docid: 47838
negative_passages.text: Lemma 3.3-7 and Theorem 3.6-2 in Kreyszig's "Introductory Functional Analysis With Applications": What if completeness is lost?
negative_passages.docid: 118049
negative_passages.text: Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
negative_passages.docid: 66630
negative_passages.text: Proof of Mazurkiewicz theorem
negative_passages.docid: 131992
negative_passages.text: A problem on continuous functions
negative_passages.docid: 142014
negative_passages.text: study of subspace generated by $f_k(x)=f(x+k)$ with f continuous, bounded..
negative_passages.docid: 30510
negative_passages.text: Second mean value theorem proof
negative_passages.docid: 35281
negative_passages.text: $1992$ IMO Functional Equation problem
negative_passages.docid: 28731
negative_passages.text: Banach space in functional analysis
negative_passages.docid: 73254
negative_passages.text: spectral radius in normed space is subadditive.
negative_passages.docid: 81974
negative_passages.text: Let $f_1 , f_2: I\mapsto \mathbb{R}$ bounded functions. Show that $L(f_1)+L(f_2)\leq L(f_1+f_2)$ (Riemann integral)
negative_passages.docid: 135650
negative_passages.text: Sequences in Hilbert spaces
negative_passages.docid: 147021
negative_passages.text: Proving a function is 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: 97994
negative_passages.text: Orthogonality Relations Exercise, Brezis' Book Functional Analysis