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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Spring 2016 • Question 5

Question

Math 6210 • Real Analysis Spring 2016 • Question 5

Consider \(\ell ^4(\mathbb N)\) equipped with topology induced by the norm \(\lVert \cdot \rVert _4\). Show that there exists an open set in this topology that is not open in the weak topology on \(\ell ^4(\mathbb N)\).

Raw LaTeX

Consider \(\ell^4(\mathbb N)\) equipped with topology induced by
the norm \(\lVert\cdot\rVert_4\). Show that there exists an open set in this
topology that is not open in the weak topology on \(\ell^4(\mathbb N)\).

Topic Tags

Lp Spaces and Sequence Spaces Weak Topologies and Weak Convergence