The existence theorem of random vector-valued measures and one in another form that is conveinent for use are showed.We substitute the two- point distribution in the expression of the thinning operator by a probabi- l...The existence theorem of random vector-valued measures and one in another form that is conveinent for use are showed.We substitute the two- point distribution in the expression of the thinning operator by a probabi- lity measure on (the index set may be uncountable),and obtain what we call mark accumulator mapping,its existence having been proved by use of the existence theorems mentioned above.we parallelly extend almost all properties of the thinning operator to the mark accumulator mapping.展开更多
In this paper,we study mainly properties of a class approx mate ope rator in Hilbert space, form as S=T+Q where T is a power class (N) operator and Q is a quasinilpotent opera tot with TQ=QT. We discuss relation of ke...In this paper,we study mainly properties of a class approx mate ope rator in Hilbert space, form as S=T+Q where T is a power class (N) operator and Q is a quasinilpotent opera tot with TQ=QT. We discuss relation of kernel of operator S and T and Q, while discuss properties of its spectrum by using the ultraproduct theory and prove that for a bounded sequence of point {x_n} in H,Sx_n→O iff Tx_n→O and Qx_n→O.展开更多
文摘The existence theorem of random vector-valued measures and one in another form that is conveinent for use are showed.We substitute the two- point distribution in the expression of the thinning operator by a probabi- lity measure on (the index set may be uncountable),and obtain what we call mark accumulator mapping,its existence having been proved by use of the existence theorems mentioned above.we parallelly extend almost all properties of the thinning operator to the mark accumulator mapping.
文摘In this paper,we study mainly properties of a class approx mate ope rator in Hilbert space, form as S=T+Q where T is a power class (N) operator and Q is a quasinilpotent opera tot with TQ=QT. We discuss relation of kernel of operator S and T and Q, while discuss properties of its spectrum by using the ultraproduct theory and prove that for a bounded sequence of point {x_n} in H,Sx_n→O iff Tx_n→O and Qx_n→O.
