IN THIS PAPER WE INTRODUCE A NEW MODEL OF A BLOCK MATRIX operator  M (G,H) INDUCED BY TWO SEQUENCES G AND H. THEN BY ITS CORRESPONDING COMPOSITION operator CT ON L2+=L2 (N0) WE CHARACTERIZE P-PARANORMALITY THE BLOCK MATRIX operator M (G,H).

IN THIS PAPER, WE GIVE SOME NECESSARY AND SUFFICIENT CONDITIONS FOR WEIGHTED Conditional expectation TYPE operatorS ON L2 (S) TO BE CENTERED. ALSO, WE PROVE THAT THE ALUTHAGE TRANSFORMATION OF ANY WEIGHTED Conditional expectation TYPE operator IS CENTERED.

IN THIS PAPER, WE INVESTIGATE SOME THE ALGEBRAIC STRUCTURE OF TU(¦) = U * ¦, SO-CALLED LAMBERT operator ON L2(Å) SPACES, THAT U WILL BE ANY MEASURABLE AND CONDITION ABLE FUNCTION.

IN THIS NOTE, WE DISCUSS MEASURE THEORETIC WEIGHTED COMPOSITION operatorS ON L2(S) IN SOME PARANORMAL CLASSES OF operatorS. THE PLAN OF THIS NOTE IS TO PRESENT SOME CHARACTERIZATIONS OF WEAK  -PARANORMAL CLASSES OF WEIGHTED COMPOSITION operatorS ON L2(S). WE THEN GIVE SPECIFIC EXAMPLES ILLUSTRATING THESE CLASSES.

IN THIS NOTE WEIGHTED FROBENIUS-PERRON operator P AND THEIR FINITE SUMS ON L1(Å) IS CONSIDERED AND THEN, BOUNDEDNESS, COMPACTNESS AND ESSENTIAL NORM OF THESE TYPE operatorS ARE INVESTIGATED.

IN THIS ARTICLE, WE DISCUSS MEASURE THEORETIC CHARACTERIZATIONS FOR WEIGHTED COMPOSITION operatorS IN SOME operator CLASSES ON L2(S) SUCH AS, K-QUASI-PARANORMAL, QUASI-∗-PARANORMAL, P-∗-PARANORMAL AND QUASI-CLASS A BY THE LANGUAGE OF Conditional expectation operatorS. NEXT WE PRESENT AN EXAMPLE WHICH SHOWS WEIGHTED COMPOSITION operatorS CAN SEPARATE THESE CLASSES.