Compact Operators on a Hilbert Space

lunde · Jul 12, 2010

Hello, I hope I am asking this in the right area of the forums. I wanted to ask if the following formula is true (assuming H is infinite dimensional and separable):

[tex]\mathcal{K} (\mathcal{H}) \approx \mathcal{K} (\mathcal{H} \oplus \mathcal{H} \oplus \mathcal{H} \oplus \mathcal{H})\approx M_{4} (\mathcal{K} (\mathcal{H}))[/tex]

I'm pretty sure this is true, but I am worried I am crazy, because I don't understand how every compact operator could secretly be 16 compact operators

Hurkyl · Jul 12, 2010

Please only post a question once.

Compact Operators on a Hilbert Space

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Compact Operators on a Hilbert Space

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