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x** is weak* continuous iff x** Є j(ε).

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Topology

Suppose that Ε is a normed linear space. Let j: Ε→ Ε** be the canonical imbedding and let x** be a linear functional on Ε*.
Then x** is weak* continuous if and only if x** Є j(Ε).

See the attached file.

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This solution is comprised of a detailed explanation of the canonical imbedding of the normed linear space. It contains step-by-step explanation for the following problem.

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Topology

Suppose that Ε is a normed linear space. Let j: Ε→ Ε** be the canonical imbedding and let x** be a linear functional on Ε*.
Then x** is weak* continuous if and only if x** Є j(Ε).

See the attached file for the solution of the problem.

Posting 38049 reply

The intersection of any non-empty family of topologies on is a topology on .
And this topology is weaker than all the above family of topologies and stronger than any topology
which is weaker than all these topologies.
This is the greatest lower bound of this family.

Let be a non-empty class of topological spaces and for each let be a mapping of ...

Solution provided by:
Thokchom Sarojkumar Sinha, MSc
Education
  • BSc, Manipur University
  • MSc, Kanpur University
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