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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Fall 2017 • Question 2

Question

Math 6210 • Real Analysis Fall 2017 • Question 2

Prove or give a counterexample: \(B_1,B_2\) are Banach spaces and \(A:B_1\to B_2\) is continuous, linear, injective, and \(A(B_1)\) is dense. Then \(A\) is a bijection.

Raw LaTeX

Prove or give a counterexample: \(B_1,B_2\) are Banach spaces and
\(A:B_1\to B_2\) is continuous, linear, injective, and \(A(B_1)\) is dense. Then
\(A\) is a bijection.

Topic Tags

Automorphism Groups and Biholomorphisms Banach Spaces Compactness in Metric and Normed Spaces