Explore BrainMass

Explore BrainMass

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

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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.

    © BrainMass Inc. brainmass.com March 4, 2021, 6:16 pm ad1c9bdddf
    https://brainmass.com/math/geometry-and-topology/canonical-imbedding-normed-linear-space-38049

    Attachments

    Solution Preview

    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 Summary

    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.

    $2.49

    ADVERTISEMENT