A couple of thoughts on that:
I learned a while ago that "Faith" is, for practical purposes, synonymous with "Trust", and in the Christian sense, trust in the Person of God and trust in the Person of Jesus Christ. I would take the position that our trust will indeed be eternal. "Faith" also carries shades of "faithfulness" or loyalty. I contend that our loyalty will be eternal also.
"Hope" is an interesting question. Why do we get up in the morning? What keeps us keeping on? Eternity is a long time; what will sustain us day after day, century after century, eon after eon? I hope (pun intended) God will continuously have new and challenging things for us.
I believe it would depend on what we mean by faith.
It does include trust.
But is that what Hebrews means?
Faith is the essence of things hoped for,,,
Hebrews 11:1-3
1Now faith is being sure of what we hope for, being convinced of what we do not see.
2 For by it the people of old[a] received God’s commendation.[b]
3 By faith we understand that the worlds[c] were set in order at God’s command,[d] so that the visible has its origin in the invisible.
Faith makes us be sure of what we hope for.
What do we hope for?
Isn't it God's promise of heaven at the end of our lives??
Faith makes us be convinced of things not seen.
I get on an elevator in faith that it will take me to the top floor.
When I'm at the top floor,,,
do I still need faith?
Trust, I think, would be an ELEMENT of faith.
If we have faith in someone, we will trust that person.
Yes,,,,definitely this trust will continue forever.
But does faith mean only trust?
Hope, biblically speaking, is the hope we have of achieving our salvation,,,our glorification.
Once achieved,,,do we still need hope of achieving it?
IOW,,,I THINK you might be applyiing the common understanding of hope and not the biblical undersanding.
And I think that biblically faith is more than trust in a person but in an entire belief system that will no longer be necessary in heaven.
I looked up some definitions on the net...I think the following is correct:
Biblically, faith is considered a belief and trust in God based on good evidence but without total proof. To have faith, we must trust that God is there and working on our behalf, even though we can't see him. In fact, the word “faith” comes from the Latin word “fidere,” which means “to trust.”
(forgot to get the source..sorry).
QotQuestions includes your definition:
Faith resides at the core of Christianity and the Christian life. While the Bible has much to say about it, faith is a challenging concept to define. A biblical definition of faith reaches beyond mere belief—the simple acknowledgment that God exists—into the realm of trust. Genuine faith involves abandoning all human reliance on self-efforts and placing total dependence upon God’s character, His actions, and His promises, as revealed in His Word.