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Is it possible for a sequence of matrices to have pointwise but not uniform convergence?

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Is it possible for a sequence of matrices to have pointwise but no uniform convergence?

The norm for the matrices is the operator norm.

linear-algebra matrices functional-analysis limits uniform-convergence

share|cite|improve this question

asked Mar 14 at 20:38

Jens WagemakerJens Wagemaker

581312

$endgroup$

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  Your title and the content of the question contradict one another. Which is the actual question? Edit: Ignore this. Its been fixed
  $endgroup$
  – JEET TRIVEDI
  Mar 14 at 20:39
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  It should be fixed now.
  $endgroup$
  – Jens Wagemaker
  Mar 14 at 20:40
  

  
  
  
  


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  In finite dimensions? No. In infinite dimensions? Yes.
  $endgroup$
  – s.harp
  Mar 14 at 20:52
  
  
  

  
  
  
  


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  $begingroup$
  This was exactly what it was about. And what do you mean with infinite dimensions? I.e. what is a matrix in infinite dimensions?
  $endgroup$
  – Jens Wagemaker
  Mar 14 at 20:59
  
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Recall that a matrix with respect to a basis in finite dimensional spaces has columns given by $Te_1, Te_2, cdots Te_n$ where $T$ is the linear transformation in question. If you have a linear operator between two spaces where the idea of a basis makes sense (between two Hilbert spaces for example) then you can construct a matrix in a similar way.
  $endgroup$
  – rubikscube09
  Mar 18 at 5:34
  
  
  

  
  
  
  

add a comment | 

0

$begingroup$

Is it possible for a sequence of matrices to have pointwise but no uniform convergence?

The norm for the matrices is the operator norm.

linear-algebra matrices functional-analysis limits uniform-convergence

share|cite|improve this question

asked Mar 14 at 20:38

Jens WagemakerJens Wagemaker

581312

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Your title and the content of the question contradict one another. Which is the actual question? Edit: Ignore this. Its been fixed
  $endgroup$
  – JEET TRIVEDI
  Mar 14 at 20:39
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  It should be fixed now.
  $endgroup$
  – Jens Wagemaker
  Mar 14 at 20:40
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  In finite dimensions? No. In infinite dimensions? Yes.
  $endgroup$
  – s.harp
  Mar 14 at 20:52
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  This was exactly what it was about. And what do you mean with infinite dimensions? I.e. what is a matrix in infinite dimensions?
  $endgroup$
  – Jens Wagemaker
  Mar 14 at 20:59
  
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Recall that a matrix with respect to a basis in finite dimensional spaces has columns given by $Te_1, Te_2, cdots Te_n$ where $T$ is the linear transformation in question. If you have a linear operator between two spaces where the idea of a basis makes sense (between two Hilbert spaces for example) then you can construct a matrix in a similar way.
  $endgroup$
  – rubikscube09
  Mar 18 at 5:34
  
  
  

  
  
  
  

add a comment | 

$begingroup$

Is it possible for a sequence of matrices to have pointwise but no uniform convergence?

The norm for the matrices is the operator norm.

linear-algebra matrices functional-analysis limits uniform-convergence

share|cite|improve this question

asked Mar 14 at 20:38

Jens WagemakerJens Wagemaker

581312

$endgroup$

share|cite|improve this question

asked Mar 14 at 20:38

Jens WagemakerJens Wagemaker

581312

share|cite|improve this question

asked Mar 14 at 20:38

Jens WagemakerJens Wagemaker

581312

asked Mar 14 at 20:38

Jens WagemakerJens Wagemaker

581312

asked Mar 14 at 20:38

Jens WagemakerJens Wagemaker

581312