query: Weakly convergent but not strongly convergent sequence in $L^2(\Bbb R^n)$.
positive_passages.docid: 143642
positive_passages.text: Does the sequence $(\sqrt{n} \cdot 1_{[0, 1/n]})_n$ converge weakly in $L^2$?
negative_passages.docid: 113790
negative_passages.text: $\overline{B_1(0)}$ is not weakly* sequentially compact in $(l^\infty)$'
negative_passages.docid: 147661
negative_passages.text: Show that {$x_n$} is a convergent sequence if $d(x_{n+2}, x_{n+1})≤ rd(x_{n+1}, x_n)$
negative_passages.docid: 40820
negative_passages.text: Weak convergence in separable Hilbert spaces
negative_passages.docid: 30488
negative_passages.text: Convergence of a sequence implies convergence of the norm of the sequence
negative_passages.docid: 13827
negative_passages.text: Uniform convergence for sequences of functions
negative_passages.docid: 73934
negative_passages.text: Subadditive sequences and the limit $\sup_{n\to\infty} a_n / n$
negative_passages.docid: 138317
negative_passages.text: weak convergence in $l^p$ implies bounded and pointwise convergence
negative_passages.docid: 117764
negative_passages.text: Almost surely convergence of the sequence
negative_passages.docid: 127224
negative_passages.text: Sequence uniform convergence but the derivatives are not.
negative_passages.docid: 132140
negative_passages.text: Convergence of Sequence of Real Numbers
negative_passages.docid: 49507
negative_passages.text: Is this sequence convergent?
negative_passages.docid: 64721
negative_passages.text: A Sequence converges to a limit $L \in \mathbb R$ if, and only if, an $N$-th tail of the sequences converges to $L$ for some $N \in \mathbb N$
negative_passages.docid: 86319
negative_passages.text: Give an example of a bounded, non-convergent real sequence $(a_n)$ s.t. $a_n-a_{n-1}\rightarrow 0$
negative_passages.docid: 129087
negative_passages.text: Proof that a sequence of continuous functions $(f_n)$ cannot converge pointwise to $1_\mathbb{Q}$ on $[0,1]$
negative_passages.docid: 135450
negative_passages.text: Prove $x^n$ is not uniformly convergent
negative_passages.docid: 15319
negative_passages.text: Convergence of recurrence sequence