3) Let {rn : n e N} be a basis in a normed space X. Show that X is not a Banach space. (Hint: Apply Baire's Lemma to the subspaces En = span{r1,12,...,In})

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 4AEXP
icon
Related questions
Question
3) Let {tn : n E N} be a basis in a normed space X. Show that X is not a
Banach space. (Hint: Apply Baire's Lemma to the subspaces En = span{r1,x2, ..., xn})
Transcribed Image Text:3) Let {tn : n E N} be a basis in a normed space X. Show that X is not a Banach space. (Hint: Apply Baire's Lemma to the subspaces En = span{r1,x2, ..., xn})
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Inner Product Spaces
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning