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Aug 4 at 14:19 comment added Antonius You might want to look at G.L. Litvinov, "On the traces of linear operators in locally convex spaces" Sel. Math. Sovietia , 8 : 3 (1989) pp. 203–212 Trudy Sem. Vekt. i Tenz. Anal. , 19 (1979) pp. 243–272
Aug 3 at 0:20 history edited WillG CC BY-SA 4.0
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Aug 2 at 17:27 history edited WillG CC BY-SA 4.0
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Aug 2 at 16:16 comment added WillG @Nandor I have edited the post to clarify what I mean by $\pi_n$. The formula I have given is then just the trace formula in the finite-dimensional case (extended to Schauder bases), no?
Aug 2 at 16:14 history edited WillG CC BY-SA 4.0
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Aug 2 at 16:08 comment added Antonius Which kind of projection do you mean? Orthogonal? Or with respect to the given basis? Next, your formula looks weird, as the trace is a number and the projection must be vector-valued, hence the right hand side is a vector.
Aug 2 at 15:32 history asked WillG CC BY-SA 4.0