## A question related to spectral decomposition

Suppose that $$(\mathcal{A},\Phi)$$ is a semifinite von Neumann algebra with trace $$\Phi$$, $$B$$ is a positive self adjoint operator affiliated with $$\mathcal{A}$$, $$X$$ is a positive operator with $$\Phi(X)<\infty$$ that commutes with $$B$$, and $$E_n$$‘s are an increasing sequence of spectral projections of $$X$$ with $$\Phi(E_n)<\infty$$ and $$\lim E_n=s(X)$$, where $$s(X)$$ denotes the support of $$X$$. Let $$BX=\int_0^\infty \lambda dP(\lambda)$$ be the spectral resolution for $$BX$$. Then $$BXE_n=\int_0^\infty \lambda dP_n(\lambda)$$ where $$I-P_n(\lambda)=(I-P(\lambda))E_n$$. Why is it true that $$\Phi(BXE_n)=\int_0^\infty \Phi(I-P_n(\lambda))d\lambda?$$

## Security question: What questions do you ask?

Working on a save quote feature for our new website, one of the security requirements is to ask a secret question and obtain a value from the user.

Does anyone have suggestions on the type of Security questions to ask?

by: AntuSEO
Created: —
Viewed: 163

## I have a question about domain transfer

Hi,
this may seem a newbie question but this is confusing for me.
If anyone can explain this, I would be greatful.

I have this website (domain+hosting) with a company. registered on Sep 18, 2018 for one year.
The hosting package + domain is going to expire on Sep 17, 2019.
I want to keep this domain but not with this company.
So do I have to transfer this domain or renew with another company?
And when?
If I transfer this domain to new company, today on June 23, 2019.
Will it be…

I have a question about domain transfer

## [ Politics ] Open Question : What is your opinion on Democrat candidate Marianne Williamson?

https://www.ontheissues.org/Marianne_Williamson.htm

## [ Politics ] Open Question : What is your opinion on Democrat candidate Marianne Williamson?

https://www.ontheissues.org/Marianne_Williamson.htm

## [ Renting & Real Estate ] Open Question : Construction loan to mortgage loan. Can I get locked rate?

Looking into getting a construction loan that we will transfer to mortgage. Can I get pre-approval for the loan and have a locked in rate for the mortgage? Or does the mortgage rate go based on when the house is completed and we transfer the loan to the mortgage?