in a hopeful manner
informal it is hoped; I hope
Hopefully he will arrive in time
Though the use of hopefully as a sentence adverb in the sense, ‘it is to be hoped (that); let us hope’ in sentences such as Hopefully, they'll be home before it gets dark is still decried by traditionalists in Britain and America, it has generally established itself as part of normal usage. However, It is interesting to note, however, that opposition to such words as frankly and regretfully with a similar function has not been expressed. So while it may appear unnecessarily restrictive to reserve the use of the word to such constructions as She eyed the plate of jam tarts hopefully it is probably better to limit it the sentence adverb use of hopefully to informal or spoken contexts