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Abstract
Some results about inversion formula of functional operator with generalized dilation are given. By means of commutative Banach algebra theory the explicit form of inversion operator is expressed. Some commutative Banach algebras with countable generator systems are constructed, their maximal ideal spaces are investigated.
Straipsnyje nagrinejama vieno apibendrinto operatoriaus apvertimo problema. Naudojantis komutatyviaja Banacho algebros teorija, sudaryta atvirkštinio operatoriaus išreikštine skaičiavimo formule. Sukonstruotos kelios komutatyvines Banacho algebros, kuriu generuojančios sistemos yra suskaičiuojamos. Pagrindineje teoremoje pateiktos būtinos ir pakankamos salygos, kad funkcinis operatorius turetu atvirkštini.