Spectral theorem for Bounded Self-Adjoint Linear operators
Let $T:\mathcal H\rightarrow \mathcal H$ be a bounded self-adjoint linear operator on a complex Hilbert space $\mathcal H$.Then $T$ has the spectral representation $$T=\int_{m-0}^M\lambda dE_{\lambda}$$ Where $\mathcal E=(E_\lambda)$ is the spectral family associated with $T,$the integral is to be understood in the sense of uniform operator convergence,and for all $x,y\in \mathcal H$,$$\langle Tx,y\rangle=\int_{m-0}^M\lambda dw(\lambda)$$
Where the integral is an ordinary Riemann Stieltjes integral.
This theorem is given in Kryszig's functional analysis text book.I am trying to understand it but not getting it ...Can someone explain it via an example?