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edited May 14, 2013 at 13:10

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HiFor an discrete (separable) infinite-dimensional Hilbert Space with a compact operator, 0 is always an accumulation point (https://www.math.ucdavis.edu/~hunter/book/ch9.pdf).

For an discrete (separable) infinite-dimensional Hilbert Space with a compact operator, 0 is always an accumulation point (https://www.math.ucdavis.edu/~hunter/book/ch9.pdf). Does this mean its part of a spectrum? Also can it be an eigenvalue? Otherwise, how should I prove it is/isnt?

ThanksDoes this mean its part of a spectrum? Also can it be an eigenvalue? Otherwise, how should I prove it is/isnt?

Hi,

For an discrete (separable) infinite-dimensional Hilbert Space with a compact operator, 0 is always an accumulation point (https://www.math.ucdavis.edu/~hunter/book/ch9.pdf). Does this mean its part of a spectrum? Also can it be an eigenvalue? Otherwise, how should I prove it is/isnt?

Thanks

For an discrete (separable) infinite-dimensional Hilbert Space with a compact operator, 0 is always an accumulation point (https://www.math.ucdavis.edu/~hunter/book/ch9.pdf).

Does this mean its part of a spectrum? Also can it be an eigenvalue? Otherwise, how should I prove it is/isnt?

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asked May 14, 2013 at 13:06

user33960

Can an accumulation point be an eigenvalue?

Hi,

For an discrete (separable) infinite-dimensional Hilbert Space with a compact operator, 0 is always an accumulation point (https://www.math.ucdavis.edu/~hunter/book/ch9.pdf). Does this mean its part of a spectrum? Also can it be an eigenvalue? Otherwise, how should I prove it is/isnt?

Thanks